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1995 | 71 | 4 | 381-389
Tytuł artykułu

On the converse of Wolstenholme's Theorem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
71
Numer
4
Strony
381-389
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-03-21
poprawiono
1994-12-02
Twórcy
  • Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2
Bibliografia
  • [1] H. W. Brinkmann, Problem E.435, Amer. Math. Monthly 48 (1941), 269-271.
  • [2] V. Brun, J. Stubban, J. Fjeldstad, R. Lyche, K. Aubert, W. Ljunggren and E. Jacobsthal, On the divisibility of the difference between two binomial coefficients, in: Den 11te Skandinaviske Matematikerkongress, Trondheim, 1949, 42-54.
  • [3] J. Buhler, R. Crandall, R. Ernvall and T. Metsänkylä, Irregular primes and cyclotomic invariants to four million, Math. Comp. 61 (1993), 151-153.
  • [4] M. D. Davis, Hilbert's tenth problem is unsolvable, Amer. Math. Monthly 80 (1973), 233-269.
  • [5] L. E. Dickson, The History of the Theory of Numbers, Vol. 1, Chelsea, New York, 1966.
  • [6] H. M. Edwards, Fermat's Last Theorem, Springer, New York, 1977.
  • [7] J. W. L. Glaisher, Congruences relating to the sums of products of the first n numbers and to other sums of products, Quart. J. Math. 31 (1900), 1-35.
  • [8] J. W. L. Glaisher, On the residues of the sums of products of the first p-1 numbers, and their powers, to modulus p² or p³, Quart. J. Math., 321-353.
  • [9] R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1981.
  • [10] W. Johnson, Irregular primes and cyclotomic invariants, Math. Comp. 29 (1975), 113-120.
  • [11] W. Johnson, p-adic proofs of congruences for the Bernoulli numbers, J. Number Theory 7 (1975), 251-265.
  • [12] J. P. Jones, Private correspondence, January 1994.
  • [13] J. P. Jones and Yu. V. Matijasevič, Proof of recursive unsolvability of Hilbert's tenth problem, Amer. Math. Monthly 98 (1991), 689-709.
  • [14] E. E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math. 44 (1852), 93-146.
  • [15] E. Lehmer, On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson, Ann. of Math. 39 (1938), 350-360.
  • [16] E. Lucas, Sur les congruences des nombres eulériens et des coefficients différentiels des fonctions trigonométriques, suivant un module premier, Bull. Soc. Math. France 6 (1878), 49-54.
  • [17] Yu. V. Matijasevič, Enumerable sets are diophantine, Dokl. Akad. Nauk SSSR 191 (1970), 279-282 (in Russian); English transl. with addendum: Soviet Math. Dokl. 11 (1970), 354-357. MR 41, #3390.
  • [18] Yu. V. Matijasevič, Primes are non-negative values of a polynomial in 10 variables, Zap. Nauch. Sem. Leningrad. Otdel. Mat. Inst. Akad. Nauk SSSR 68 (1977), 62-82 (in Russian); English transl.: J. Soviet Math. 15 (1981), 33-44.
  • [19] Yu. V. Matijasevič and J. Robinson, Reduction of an arbitrary diophantine equation to one in 13 unknowns, Acta Arith. 27 (1975), 521-553.
  • [20] R. J. McIntosh, A generalization of a congruential property of Lucas, Amer. Math. Monthly 99 (1992), 231-238.
  • [21] R. J. McIntosh, Congruences identifying the primes, Crux Mathematicorum 20 (1994), 33-35.
  • [22] P. Ribenboim, 13 Lectures on Fermat's Last Theorem, Springer, New York, 1979.
  • [23] P. Ribenboim, The Book of Prime Number Records, 2nd ed., Springer, New York, 1989.
  • [24] E. T. Stafford and H. S. Vandiver, Determination of some properly irregular cyclotomic fields, Proc. Nat. Acad. Sci. U.S.A. 16 (1930), 139-150.
  • [25] J. W. Tanner and S. S. Wagstaff, Jr., New congruences for the Bernoulli numbers, Math. Comp. 48 (1987), 341-350.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav71i4p381bwm
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