Combinatorial congruences modulo prime powers

• Autores: Zhi-Wei Sun, Donald M. Davis
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 11, 2007, págs. 5525-5553
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04236-5
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• Resumen

  • Let be any prime, and let and be nonnegative integers. Let and . We establish the congruence (motivated by a conjecture arising from algebraic topology) and obtain the following vast generalization of Lucas' theorem: If is greater than one, and are nonnegative integers with , then We also present an application of the first congruence to Bernoulli polynomials and apply the second congruence to show that a -adic order bound given by the authors in a previous paper can be attained when .