Congruences of multiple sums involving invariant sequences under binomial transform

2009/11/05 by Roberto Tauraso, Tauraso, Roberto
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.NT #msc:05A10 #msc:05A19 #msc:11A07 #msc:11B65

paper · pdf · doi:10.48550/arxiv.0911.1074

arxiv created 2009/11/05 · arxiv updated 2009/12/01

Abstract

We will prove several congruences modulo a power of a prime such as ∑_0<k₁<...<k_n<p\legp-k_n3 (-1)^k_n\over k₁... k_n≡ lll -2ⁿ⁺¹+2\over 6ⁿ⁺¹ p B_p-n-1(1\over 3) \pmodp² if n is odd -2ⁿ⁺¹+4\over n6ⁿ B_p-n(1\over 3) \pmodp if n is even. where n is a positive integer and p is prime such that p>max(n+1,3).

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