Index of Authors Cited

The names appearing here are those of authors whose works are referred to in this volume. References occur at the end of each problem (e.g. D11, pp. 90-93); in the Introduction, I (pp. 1-2) and at the beginning of Sections A (pp. 3-4), D (p. 79), E (p. 110) and F (p. 132). Mentions unsupported by references are listed in the General Index.

Abbott, Harvey L. B2, C16, ElO, EIl, E12

Acland-Hood F4 Adena, Michael A. F4 Adleman, Leonard M. A Aho, A.V. DIl Aigner, A. D11 Ajtai, M. C9 van Albada, P.J. DIl Alanen, Jack B4, B6 Alex, Leo J. DlO Alladi, Krishnaswarni B22 Almering, J.H.J. D20 Alter, Ronald B37, C12, D27 Anderson, David Brent F4 Andrews, George E. A3, E30 Ang, D.D. D20 AngelI, I. O. A2 Archibald, R.C. A3 Arshon, S. E21 Artuhov, M.M. B2, B4 Atkin, A. Oliver L. A8 Aull, C.E. B2

Baillie, Robert A3, A8, AB, B21 Baker, T. D15 Ball, W.W. Rouse F4 Barbeau, E.J. Dll

Barnett, J.A. C12 Barrucand, P.-A. F7 Bastien, L. D27 Bate, J.A. C12 Bateman, Paul T. B2, B25, C7 Baumert, L.D. ClO, Ell Baumgartner, J. E29 Bays, Carter A4 Bear, Robert B2 Bear, Robert B2 Beck, Walter E. B5 Beeger, N.G.W.H. A12 Beeler, Michael D. B7, ElO, E16 Behrend, F.A. ElO Bender, Edward A. D6 Benkoski, S.J. B2 Berge, Claude C18 Berlekamp, Elwyn Ralph C7, ElO, E26,

E27 Berman, Paul C18 Bernstein, Leon D8, Dll Besicovitch, A.S. D20, E5 Best, M.R. C10, D7 Beyer, Ö. C7 Birch, Brian J. D1, D27 Blass, J. D6 Bleicher, M.N. Dll Bludov, V.S. C8 Blundon, W.J. A6, D5, D18

149

150

Bode, Dieter B9 Böhm, Corrado EI6 Bohman, Jan C20 Bombieri, Enrico A8 Borho, Walter B4, B7 Boming, Alan A2 Bose, Raj C. C9, Cll Boyle, R.D. FI5 BratIey, P. B4 Brauer, Alfred B28, C6, C7, F5 Braunholtz, C.H. E21 Bremner, Andrew D I Brenner, Joel L. DIO Brent, Richard P. A, A3, A8 Breusch, Robert Dll Briggs, W.E. C3 Brillhart, John A3 Brocard, H. D25 Bromhead, T. DI8 Brouwer, A.E. CIO Brown, Alan L. B2 Brown, B.H. B4 Brown, Ezra B2 Brown, Thomas C. EIO, E21 Brudno, Simcha D I Bruen, A. CI8 Bumside, William S. DlI, DI8 Burshtein, N. Dll, FI4 Buschman, R.G. C3 Buxton, M. BI Bymes, J.S. C7

Cadwell, J.H. A8 Campbell , Paul J. D 11 Carlitz, Leonard B44 Carmichael, R.D. A12, B39 Cassels, J.W.S. Dll, Dl2, D27, F, F22 Catalan, E. B6 CatIin, P.A. B41 Catteneo, Paolo B2 Chan, C. CI2 Chandra, Ashok K. EIO Chao Ko D13 Chase, A.B. Dll Chein, E.Z. BI, D18, FI5 Chen Jing-Run A8, CI, FI Chinburg, Ted B25 Choi, S.L.G. B26, C14, EIl, F13

Index of Authors Cited

Chowla, Sardomon A6, C4, C9, Cll, D4, E28

Churchouse, R.F. FI3 Chvatal, Vaclav EIO Cipolla, M. AI2 Cohen, Fred A19, FI3 Cohen, Graeme L. BI, B2, B37 Cohen, Henri B7 Cohen, Robert Dll Cohn, Harvey Cohn, J.H.E.

D12, F7 D6

Comtet, Louis F17 Condict, J. T. BI Conway, John Horton C7, C8, D18,

El7, E26, E27, F26 Cook, R.J. A8 Cook T.J. B3 Cormack, G.V. B21 van der Corput, J.G. CI Costello, Patrick B4 Coxeter, Harold Scott Macdonald D18,

F4 Craggs, D. F4 Cramer, Harald A8 Crandall, R.E. A8, EI6 Crittenden, Richard B. E23 Crocker, R. A19 Cross, J.T. B2 Cudakov, N.G. CI Culpin,D. Dl1 Curtiss, D.R. Dll Curtz, Thadeus B. D27 Cusick, T.W. Dl2

Dandapat, G.G. BI Davenport, Harold A8, D4, E20, F5,

F22 David, Richard B7 Davis, J.A. EIO, E33 Daykin, David E. D20 Dean, Richard A. E21 Dekking, F.M. E21 Dem 'janenko, V. A. Dl Deuber, Walter E14 Devitt, John StanIey B6 Diananda, P. H. CI4 Dickson, Leonard Eugene Al7, B6,

Dll, D12, D18, D27, E32

Index of Authors Cited

Ding Xia Xi Cl Dirksen, P.H. E20 Dixon, John D. A Dixon, R. C18 Dobson, Annette E20 Dudeney, Henry Ernest D3, F4

Ecklund, Earl F. B23, B33 Edgar, Hugh Maxwell D8 Edwards, Harold M. D2 Eggleton, Roger Benjamin B23, D19,

E27 Ellison, W.J. D5 Elmore, S. BI Entringer, R.C. ElO, E21, E33 Erdös Pli! I, A5, A6, A9, All, A12,

A13, A18, A19, B2, B4, B6, B8, B9, BIO, Bll, B14, B16, B18, B21, B22, B23, B26, B27, B30, B31, B32, B35, B36,B39,B40,B41,B46,C3,C6,C7, C8,C9,C10,C15,CI6,C17,D2,D4, 07, Dll, 017, D25, E, E2, E3, E4, E5,EI0,E21,E24,E31,F2,FI3,FI5. FI8

Escott, E.B. B4 Estermann, Theodore Cl Evans, Ronald J. B28, D19 Evans, Trevor A. CI0 Evdokimov, A.A. E21 Everett, C.J. E16 Everts, F. EIO EwelI, John BI, C5

Fast, H. I Faulkner, Marilyn B33 Fejes Toth, Laszlo F Fife, Earl Dennet E21 Fine, Nathan J. D19 Finkelstein, Raphael D3 Forbes, A. B5 Forman, W. E19 Foster, Lorraine L. D 10 Fraenkel, Aviezri S. C5, D8, F14 Franceschine, Nicola Dll Franqui, Benito B2 Fredericksen, H. Eil Frey, H.A.M. B3

Frobenius, G. D 12 Fröberg, Carl-Erik C20 Fuchs, W.H.J. C9 Furstenberg, H. EIO

Gallagher, Patrick X. A19 Garcia, Mariano B2, B4 Gardiner, Verna L. C3, D5 Gardner, Martin Al, A2, A3, 018,

E16, F4 Garner, Lynn E. E16 Genocchi, A. D27 Gerardin, A. D27 Gerver, Joseph L. A5, EIO Gill, C. D15 Gillies, Donald B. A3 Gioia, A.A. B4, C6 Giuga, Giuseppe A17 Godwin, H. James A2, D27 Goldberg , Michael F4

151

Golomb, Solomon W. A2, B16, 011 Golubev, V.A. A5 Gordon, Basil C5 Gosper, R. William B7, E16 Gostin, Gary B. A3 Gottschalk, W.H. E21 Graham, Ronald L. I, A3, B23, B30,

B33, C7, C9, ClO, Dl1, EIO, E30, E31, E33, F15

Griffiths, D. Oll Grimm, C.A. B32 Grinstead, Charles B22 Grosswald, Emil A5 Grun, O. BI Gupta, Hansraj C8 Guy, Michael John Thirian F26 Guy, Richard Kenneth A, B6, B8, B13,

C7, C8, E26, E27, F2, F4 Györy, K. D7

Hagis, Peter A5, BI, B2, B4, B5, B8, B37

Hahn, L-S. Oll Haight, J. F13 Hajos, G. EIO Halberstam, Heini I, A5, C9, E Haies, Alfred W. EIO

152

Hall, 1.1. ClO Hall, Marshall C 10 Hall, Richard R. B36, B39, B4I, F4 Halleyburton, John C. A3 Hammer, Joseph F Hämmerer, N. CI2 Hanani, Haim C 10 Hancock, J. DI8 Hansche, B. CI8 Hansen, W. C6 Hanson, Denis EIO, EIl Harborth, Heiko B28 Hardy, Godfrey Harold Al, D4 Härtter, E. CI2 Hawkins, David C3, E21 Heap, B.R. C7 Heath-Brown, D.R. A5, A8 Hedlund, Gustav A. E21 Heilbronn, Hans CI5 Heimer, R.L. CI2 Hendy, Michael D. BI, B2 Henricksen, Melvin B25 Hensley, Douglas A9 Heppner, E. EI6 Herzberg, Norman P. D6 Hili, Jay Roderick Al3 HilIe, J.W. Dll Hindman, Neil E29 Hofmeister, G. CI2 Holte, R. A Holton, Derek A. F4 Holzer, Ludwig Dll Hooley, Christopher B39, B40 Homfeck, B. B2 Hudson, Richard H. A4, F5 Huff, G.B. CI8 Hughes-Jones, R. F4 Hunsucker, J.L. BI, B9, Bl3 Huxley, Martin, N. A8

II'in, A.M. C6 Inkeri, K. D2 Irving, R.W. EIl Ivic, Aleksandar A8 Iwaniec, Henryk Al, A8, B39

Jabotinsky, Eri C3 Jackson, D.E. E2I, F4

Index of Authors Cited

Jensen, A.J.E.M. ClO Jerrard, R.P. B2 Jewitt, R.I. ElO Johannessen, Dag Magne Dll Johnson, WeHs D2 Joint, W. Howard DI8 Jollensten, Ralph W. DII Jones, M.F. A6 Jordan, James H. AI6, FI3 Judd, J.S. A Justin, J.S. A Jutila, Matti A8

Kac, Marc BI4 Kalbfleisch, J.G. ClO Kanold, Hans-Joachim BI, B2, B4,

B9 Kaplansky, Irving D I Karst, Edgar A5 Kay, David C. EI6 Keller, O.H. F Kellogg, O. D. Dli Kelly, Patrick A. F4 Kendall, David G. B2 Khinchin, A. Y. ElO Killgrove, Raymond B. AlO Kishore, Masao B2, B37 Kiss, E. Dli Klamkin, Murray S. B2 Klamer, David A. CI8 Klee, Victor L. B39 Klotz, W. CI2 KI\2ive, Torleiv F4 Knapowski, S. A4 Knödel, W. Al3 Knuth, Donald C6 Kolen, A.W.J. ClO KomIos, J. C9, EIl Kovach, Ladis D. D 11 Kraitchik, Maurice A3, C18, DI8,

D25 Kravitz, Sidney A2, B2 Krückeberg, F. C9 Krukenberg, C.E. Fl3 Kubicek, Jan Dl Kubota, K.K. D27 Kurepa, f)uro B44 Kürschak, Jozsef DIl

Index of Authors Cited

Lagarias, Jeff E30 Lagrange, Jean 04, 015, 018, 027 Lai, Mohan A6, B5, B8, 05, 018 Lander, LJ. A6, A8, 01 Langenbach, H. CI2 Langevin, Michel B32 Lawson, Denis 011 Lazarus, R. C3, 05 Lebensold, Kenneth B24 Lee, E.J. B4 Leeeh, John A4, 018, E21 Lehmer, Oerrick Henry A3, A7, A8,

A12, A13, B6, B29, B37, 02, F6 Lehmer, Emma B45, F6 Lekkerkerker, C. G . F Lenstra, Hendrik Willem A Levine, Eugene E28 Lewin, Mordechai C7 Lewis, Oonald J. 06 Lieuwens, E. B37 Lindström, Bemt C8, C9, CII van Lint, Johannes H. CIO, 011 Littlewood, John Edensor AI, 04, F22 Liu, A.C. EIO Ljunggren, W. 03, 06 Lord, Graham B5, B9 Lucas, Edouard A3, 03 van de Lune, J. 07 Lunnon, W. Fred B4, CI2 Lyness, R.C. 018 Lynn, M.S. C7

Macdonald, Sheila Oates E20 Mac Mahon , Percy A. E30 Mac Williams, F. Jessie C 10 Madachy, Joseph S. B4 Mahler, Kurt 04, E18, F26 M~owski, Andrzej A12, B2, B9, B13,

B16, BI9,B25,B36, 05 Mann, Henry ClO, CI5 Marica, John FI5 Markoff, A. 012 Matthew, G. A3 Mauldon, James G. 019 McCarthy, O. CIO McCarthy, P.J. BI McOaniel, Wayne BI McKay, John B4

Me Laughlin, Philip B. A3 Mendelsohn, Nathan S. C7 Metropolis , N. C3 Mian, Abdul Majid C4, E28 Mientka, Walter E. A19, B13, E21 Miller, G.L. A Miller, Jeffrey C. P . 05 Mills, William H. B41, 013, E20,

F6 Minoli, Oaniel B2 Mirsky, L. B18, E11 Misiurewicz, M. 024 Möller, H. EI6 Montgomery, Hugh L. CI Montgomery, Peter Oll Moore, Eliakim Hastings 018

153

MordelI, Louis Joel 0, 06, 011, 018, 020,027,028

Morrison, Michael A. A3 Morse, Marston E21 Moser, Leo B33, C2, C12, C14, C17,

07, EI, EIO, E11 Motzkin, Theodor S. CI7 Mrose, Amulf C 12 Muller, P. C4 Mullin, Ronald C. CIO, C12, E20 Muskat, Joseph B. BI

NagelI, Trygve 06, 011 Nair, M. BI8 Najar, Rudolph M. B5 Nakayama, M. Oll Nathanson, Melvyn B. CI2 Nebb, Jack BI3 Newberry, R.S. B3 Newman, James R. Oll Nickel, Laura A3 Nicol, Charles A. B41, 02 Nicolas, Jean-Louis 015 Nijenhuis, A. C7 Niven, Ivan 011 Noll, Curt A3 Norrie, R. 01 Norton, Karl K. BI Noväk, Bretislav FI4

Obläth, R. 02, 011, 025 Odda, Tom E33

154

Odlyzko, Andrew M. B21, ClO, EIO Olsen, John E. CIS Ondrejka, Rudolph A3 O'Neil, Patrick E. EIO Oppenheim, Alexander D8 Ore, Oystein B2, B4 Ostmann, H. E O'Sullivan,Joseph E28 Owings, J.C. Dll

Pajunen, Seppo B2 Palama, G. DII Pan Cheng Dong CI Parkin, T.R. A6, A8, Dl Paxson, G. Aaron B6 Peacock, J. DI8 Peet, T.E. DII Penk, M.A. A8 Penney, D.E. A2 Perisastri, M. BI Peterkin, C. R. E20 Philipps, N.A. DI8 Pillai, S.S. B28 Pisano, Leonardo Dll Pleasants, P.A.B. E21 Pocklington, H.C. DI8 de Polignac, A. AI9 Pollack, Richard M. D25 Pollard, John M. A, A3 Pomerance, Carl A, AI, A5, A12, BI,

B2,B4,B9,B32,B37,B39,B46,DI9, ElO, F4

van der Poorten, Alfred J. A13, D2, FI7 Popken F26 Porubsky, Stefan E30 Poulet, Paul B2, B4, B6, B7 Pounder, J.R. Cl2 Powell, Barry J. B45 Powers, R.E. A3 Prodinger, Helmut E21 Pyateckii-Sapiro, 1.1. AI

Queneau, R. C4

Rabung, J.R. A16, EIO Rado, Richard, ElO, EI4

Index of Authors Cited

Ralston, Kenneth E. AIO, CI7 Ramachandra, K.T. B32 Ramsey, L. Thomas A5 Rankin, Robert Alasdair A8, EIO Rav, Y. Dll Recaman, Bemardo C4 Remak, R. DI2 Rennie, BasH C. E20 Renyi, Alfred A6 Richards, Ian A9 Richert, H.-E. E5 Rickert, N.W. A8 Ribenboim, Paolo D2 Riddell, James ClO, C12, EIO Rieger, G.J. B4 te Riele, H.J.J. B2, B4, B6, B8, D7 RieseI, Hans A8, C20 Rivest, R. A Robbins, H.E. E21 Robbins, Neville BI, B2 Roberts, J.B. C7 Roberts, S. D27 Robinson, Raphael, M. A3 Rödseth, Ö.J. C7 Rogers, C. Ambrose F Rohrbach, H. CI2 Root, S.C. A5, B7 Rosati, L.A. Dll Roselle, David P. E20 Rosenberger, Gerhard DI2 Ross, P.M. CI Roth, Klaus F. C9, E, ElO, F4 Rothschild, Bruce L. EIO Rotkiewicz, A. A12, Al3 Ruderman, Harry D. Dll Rumely, Robert S. A Rumney, Max B15, DI5 RusselI, W. D5 Ruzsa,I.Z. B33, EI Ryavec, Charles CI5

Salem, R. EIO Salie, Hans BI, EIO Salzer, H.E. Dll Säfközy, Andras I, E Sawyer, Warwick W. DI8 Schäffer, Juan Jorge D7 Schatz, J.A. E21

Index of Authors Cited

Schell, H. C12 Schellenberg, P.J. ClO Schinzel, Andrzej A, B9, B18, B25,

B27, B34, B36, B42, D5, D11, D23, E20, F13

Schmidt, Wolfgang M. EIO, F4 Scholz, Arnold C6 Schönheim, Johanan CIO, FI4, FIS Schroeppel, Richard B7, E16 Schuh, Fred B37 Schur, Issai B33, E11 Seah, E. A3 Sebastian, J.D. C18 Sedlacek, Jiii D11 Seelbinder, B.M. C7 Segal, S.L. D8 Selfridge, John Lewis A3, A12, A19,

B6, B21, B22, B23, B27, B30, B32, C5, C17, C18, C19, 01, 02, D17, F13

SeImer, Ernest S. C7, D 11 Sentance, W.A. B16 Servais, C. BI Shamir, A. A Shanks, Daniel I, A4, A8, BI, B13, D2 Shantaram, R. EIO Shapiro, Harold N. B2, B41, D25, E19 Shen Mok-Kong C18 Shen Tsen-Pao C18 Sheng, T.K. D20 Shippee, D.E. A3 Shiu, P. B18 Shockley, J.E. C7 Shorey, N. B32 SierpiIiski, Waclaw I, A, A5, A17, B2,

B18, B21, B36, D5, D8, Dl1, D18, D23

Simmons, Gustavus J. D25, ElO, E33 Simpson, R.J. FIS Singer, J. C9 Singmaster, David Dl1 Slater, M. C18 Sleinikov, V.1. C8 Sloane, Neil J.A. C9, ClO, Dl1, E30,

F25 Slowinski, David A3 Smith, Herschel F. A9 Smith, Paul C8 SlIJhus, T.V. Dl1 Solovay, R. A

Sontacchi, Giovanna E16 Spencer, D.C. ElO Spencer, Joel ElO Spohn, W.G. 018 Stanley, Richard P. EIO Stanton, Ralph G. ClO, C12, E20 Stark, Harold M. D26 Stearns, Robert E. B13 Stein, M.L. Cl Stein, P.R. Cl, D5 Stein, S. Dl1 Stein berg , Robert Steiner, Ray P. E16 Stemrnler, Rosemarie M. B25 Stemple, J.G. B4 Stephens, Nelson M. B25, D27 Stevens, R.S. ElO Stewart, Bonnie M. D11 Stewart, C. L. A3 Stöhr, Alfred C9, E Stolarsky, Kenneth C6 Strassen, Volker A

155

Straus, Ernst G. B2, B17, B33, C5, C6, C16, 011

Street, Anne Penfold C14, E11 Subbarao, M.V. B3, B17, B37, C6,

D11 Sudbery, A. F4 Sugunamma, M. BIS, C6 Sulyok, M. E11 Summers, T. B8 Suryanarayana, D. B2, B3, B9, B17 Swierczkowski, S. I, C17 Swinnerton-Dyer, H. Peter F. D1, F22 Sylvester, J.J. B33, C7, 011 Szekeres, George B16, B31 Szemeredi, Endre C9, CIS, C16, 04, E,

ElO, E11, E20 Szymiczek, K. A12

Temperley, Nicholas B2 Templer, Mark A2 Terras, Riho E16 Terzi, D.G. D11 Thatcher, A.W. 015 Theisinger, L. D 11 Thouvenot, J.P. ElO Thue, Axel E21

156

Thurber, Edward G. C6 Tijdeman, Robert B32, D7, D9 Tiller, G. B8 Tonascia, J. A3 Tuckerman, Bryant A3, BI Turan Pal A4, A5, All, C9, E, ElO

Uberman, V.I. C8 Ulam, Stanislaus M. I, C3, C4 Urbanek, Friedrich, J. E21 Utz, W.R. B33, C6

Vaidya, A.M. B4 Vanden Eynden, c.L. E23 Vandiver, H.S. D2 Vanstone, S.A. ClO Vamavides, P. Cl4 Vaughan, Robert C. A19, B40, Cl, Dll V6lez, William Yslas Fl5 Vinogradov, I.M. Cl Viola, C. Dil Vogt, R.L. B13 Voorhoeve, M. D7 Vucenic, W. Cl8 Vulah, L. Ja. Dl2

van der Waerden ElO Wagstaff, Samuel S. A3, A12, AB, D2 Wakulicz, A. B36 Wall, Charles R. B3, B8 Wall, D.D. A3 Wall, David W. B37 Wallis, Jennifer Seberry Eil Wallis, W.D. Ell Wang, E.T.H. El2 Wang, Yuan, Cl Ward, Morgan Dl Warren, L.J. B3

Index of Authors Cited

Watson, George Neville D3 Webb, William A. Dll Weber, J.M. B3 Weinberger, Peter A3 Weinstein, Gerald FI5 Weintraub, S. A5, A8 Weitzenkamp, R.C. AI9 Wild, K. F4 Wilf, Herbert S. C7, Dll Willans, C.P. Al7 Williams, E.R. El4 Williams, Hugh C. A, A3, A8, AB,

B21, D2, F7 Williams, Michael R. B6 Winterle, Riko Fl5 Wirsing, E. B2 Witt, E. ElO Wolke, Dieter A8 Wooldridge, Kent R. B39 Woollett, M.F.C. D5 Worley, R.T. Dll Wormell, C.P. Al7 Wright, Edmund Maitland C20 Wunderlich, Marvin C. B6, B8, C3, C4,

D8 Wybum, C.T. C6

Yamamoto, Koichi D 11 Yap Hian-Po Cl4 Yates, Samuel A3 Yorinaga, M. AB

Zachariou, Andreas B2 Zachariou, Eleni B2 Zagier, Don D 12 Zarankiewicz, Kasimierz A5 Zamke, C.R. A8 Znam, Stefan EIl, E13, Fl4 Zwillinger, Dan Cl

General Index

Names appear here if their mention in this volume is unsupported by references. Single letter entries refer to the Introduction, I(pp. 1-2) and to the beginning of Sections A (pp. 3-4), E (p. llO) and F (p. 132).

abundance B2 abundant B2 addition chain C6 additive basis C12 Alanen, Jack BIO aliquot cycIes B7 aliquot parts A aliquot sequences B6 almost perfect B2 alm ost primes A5 almost superperfect numbers B9 amicab1e numbers B4 Anderson, Claude W. 013 Argand diagram A16 arithmetic progression A5, A6, A19,

EIO, E23, E33, F13 A-sequence E28 associate A 16 augmented amicable pairs B5

barrier B8 bethrothed numbers B5 binomial coefficient B31 Bowen, Rufus 07 Boyd, Oavid E15 Brauer chain C6 Brauer number C6 Brisolis F9 Brun-Titchmarsh theorem B29

B2-sequences Buckley, M.R.

C9, E28, E32 027

Carlitz, Leonard B3 Carmichael number A12, A13, B37 Carmichael 's conjecture B39 Catalan conjecture 09 Catalan-Dickson conjecture B6 Catalan numbers B33 ceiling I Chebyshev A4 Choodnowsky D9 Chowla, I. C20 Chowla, Sardomon A4 cIass B41 cIass-number formula F5 coin problem C12 Collatz, Lothar E16 collinear integers E 10

composite A congruent A4 congruent numbers 027 continued fraction F20, F21, F22 Conway, John Horton B19, 019, E20 coprime A covering congruence A19, B21, F13 Croft, Hallard T. F23 cryptanalysis A cubic residues F7

157

158

Cullen numbers B20 Cunningham chains A 7 cycles DI8

Davenport, Harold F13, FI4 Davenport-Schinzel sequence E20 deficient B2 density E, E3, E5, E6, EIO, E26 derived cuboid DI8 determinant F27, F28 Dirichlet's theorem A distribution Fll Divis, Bohuslav F21

Ebert, Gary F8 Ecklund, Earl B31 Edgar, Hugh Maxwell D9, DIO e-divisor B 17 Eggleton, Roger Benjamin B31 Egyptian fractions Dll, FI4 Eisenstein integers AI6 Eisenstein primes A 16 e-multiperfect B 17 e-perfect B 17 Epstein's game E26 Erdös Pal A2, A15, B13, B15, B19,

B24, B34, B38, CI, C2, D9, D13, DI5, EI, E6, E7, E8, E28, E29, E33, F3, F4, F9, F16, F23, F25, F30

error-correcting codes CIO Euclid A Euler AI, DI, DI8 Eu1er numbers B45 Euler pseudoprime A 12 Euler's constant A8 Euler's totient function B8, B 11, B36,

CI, C4 exact covering system FI4 exact order C 12 exponential divisor B 17 extremal CI2

factorial A2, B13, B22, B23, B43, B44, D25, Fll

factorization A fan C13

General Index

Farey series F27 Feit-Thompson theorem R25 Fermat numbers A3 Fermat problem D2 Fermat's theorem A3, A17, B20 Fibonacci numbers A3, C4, D26 figurate numbers D3 Finucane B41 floor I Fortune's conjecture A2 fractures B41 Fried, Erwin F13 friendship graph C13 frieze patterns D 18 fundamental unit F7

Gagola, Gloria F9 Gallyas, K. D27 gaps in primes A8, All Garcia, Mariano B5 Gardner, Martin D3 Gaussian integers A 16, F13 Gaussian primes A 16 Gauss's problem FI generators D 18 Genesis B4 Gilbreath 's con jecture A 10 Godwin, H. James B6 Goldbach 's conjecture BIO, CI good primes A 14 Goormaghtigh B25 Gordon ,Basil A 16, F9, F28 graceful graph C 13 Graham, Ronald L. B37, D17, E8, E29,

E33, FIO greatest common divisor A greedy algorithm EIO, E28, E32 ' Gupta, Hansraj B33, D9, E22 Guy, Michael John Thirian C8, DI9,

EI7

Hall, Richard C 19 Hansen chain C6 Hardy, Godfrey Harold FI Hardy-Littlewood conjectures AI, A9,

CI, D4 harmonic number B2

General Index

harmonious graph C13 h-basis C12 Heegner D27 Heilbronn 's problem F4 Heron triangles D22 Hickerson, Dean B23, ClO Hilbert's tenth problem A17 Hitotumatu, Sin F24 Hofstadter, Douglas E31 Hoggatt, Vemer E. D26 Hunter, J.A.H. D27

independent C19 irrational B14, F21 irrationality sequence E24 irreducible semiperfect B2 Isaacs, Rufus B5 iteration B8, B41

Jacobi symbol F5 Jacobsthal B40 Jones, James P. B31

k-fold perfect B2 Khare, S.P. B31, B33 k-hyperperfect B2 Kleitman, Daniel J. B24 Kolba, Z. E20 Kummer B33

Lagarias, Jeffrey E8 Lam, Clement C14 Landau, Edmund I, D4, Fl lattice points ElO, F, Fl, F2, F3, F4 least common multiple B35, E2 Leech, John A9, Dll, D20 Legendre symbol Al, F5, F7 Lehmer, Derrick Henry El6, FlO, F12 Lehmer, Emma E16, FlO length C6, ClO Lenstra, Hendrik Willem B6, E15 Leonardo of Pisa D27 Littlewood, John Edensor A4, E18, F23 loopy game E26 Lucas numbers A3, C4

Lucas-Lehmer test A3 lucky numbers C3

Mahler, Kurt F27 Markoff numbers 012 Marsias, J.P. E8 Matijasevic, Ju. A17 Mauldon, James G. D16 max sequence E27 McKay, John B25 Mendelsohn, Nathan S. B21 Mersenne primes A3, BI, B9, Bll,

B15, B38 mex sequence E27 Mian-Chowla sequence E28 minimum overlap problem C17 Mirsky, L. F14 modulo A4

159

monotone arithmetic progression E33 Montgomery, Peter B3~

Mordell, Louis Joel D3, D4, F29 Moser, Leo Bll, B33, Cl, C5, C8,

014, 015, F20 Motzkin, Theodor L. A16, B19,

E22 m-perfect numbers B9 multiply perfect B2 Mycielski, Jan D9, F14

neighbor D12 Newman, Morris F14 n-fold regular E14 nim addition E27 nonaveraging set C16 noncototients B36 nondividing sets C16 nontotients B36 normal sequence E20 no-three-in-line problem F4 N -position E26

octal game E27 Odlyzko, Andrew M. E8 ordinary point D18 Ore number B2 Owens, Frank C4

160

Parker, Ernest T. B25 partial quotient F20, F22 Pell equation B 16, D 14 Penny, David E. B41 perfect cuboid D18 perfect difference set ClO perfect number BI permutation sequence E17 permutations E21, E22, E33 persistence F25 Petersen graph C 13 Platonie solids C 13 Pomerance, Carl B19, B41 van der Poorten, Alfred E15 Porubsky, Stefan F 14 postage stamp problem C12 powerful numbers B16, B17 P-position E26 prime A prime number graph A5, A14 prime number race A4 prime numbers of measurement E30,

E31 prime patterns A9 prime tripies A9 primitive abundant B2 primitive part A3 primitive pseudoperfect B2 primitive root F9 primitive solutions B 11, B 15 pseudoperfect B2, F14 pseudoprime A12, FlO Purdy, George F3

quadratie equation F27 quadratic reciprocity law F5 quadratic residue F5, F6, F8 quasi-amieable numbers B5 quasi-perfect B2 quasi-superperfect B9 queens problem C18

Rado, Richard F14 rational box D 18 recursion E 15 reduced amieable pairs B5

General Index

reflecting queens problem C18 regular E14, F7 Renyi, Alfred B9 repunit A3 residues F5, F6, F7, F8 restricted C 12 Riddell, J. F19 Riemann Hypothesis A4, A8 Riesei, Hans B20 Rudnick, Carl D9 ruler function E22

saturated configuration F2 Schinzel, Andrzej A2, B37, B39, D24 Scholz conjecture C6 Schur's conjecture F5 Schur's problem E11, E12 self-contained integer E 16 Selfridge, John Lewis A2, A18, B8,

B22, B28, B31, B33, B47, C15, Ei6, F19

Selmer conjecture D27 Shearer, J. E8 sieve of Eratosthenes C3 Silverman, David A2, B48, E8, E25 simple continued fraction F20 singular solution Dl, D12 Slavic B44 Sioane, Neil J.A. B33 sociable numbers B7 span of a set ElO squarefree A3, A19, B11, B33, F13,

F15 stepping stones A 16 Stewart, B.M. A2 Straus, Ernst B19, B22, E22, E24 strong pseudoprime A12 strongly independent C19 strongly sum-free Ei3 sum-free sets C14, E12, E13 superperfect numbers B9 Swift, Dean F13 Swinnerton-Dyer, H. Peter F. Dl symmetrie C12 Syracuse problem E16 Szemeredi, Endre F18 Szemeredi's theorem A5, C16, EI0

General Index

Taylor, H. F19 tetrahedron FI, F22 Thue sequences E21 Thue-Siegel theorem B30 Tijdeman, Robert D 17, E7 totient function B8, B 11, B36 tree C13 triangular numbers D3, D26 Turan, George C20 Turan, Paul C20, E13 twin prime conjecture A8 2-adic integer EI5

unique factorization AI6 unit A, AI6 unitary aliquot sequences B8 unitary amicable pairs B5, B8 unitary divisor B3 unitary perfect B3 unitary sociable numbers B5,

B8 untouchable numbers BIO

U-numbers C4 Usiskin, Zalman EIO

Vegh F9 Venn diagram AI2

van der Waerden 's theorem EIO Wagstaff, Samuel S. B43, B44, B48 weakly independent CI9 weight CIO weird number B2 wheel C13 Whiteman, A.L. EI9 Wilson 's theorem Al7 windmill C 13 Wolk, Barry B21 Wolstenholme's theorem B31 Woods, Alan R. B29 word CIO

Zeitlin, David C4 Z-numbers EI8

161