Congruences of multiple sums involving invariant sequences under binomial transform

Details Congruences of multiple sums involving invariant sequences under binomial transform Congruences of multiple sums involving invariant sequences under binomial transform

2009-11-05

arxiv.org/abs/0911.1074v1

Mathematics

Number Theory

Scientific paper

We will prove several congruences modulo a power of a prime such as $$
\sum_{0{lll} -{2^{n+1}+2\over 6^{n+1}} p B_{p-n-1}({1\over 3}) &\pmod{p^2} &{if $n$
is odd} -{2^{n+1}+4\over n6^n} B_{p-n}({1\over 3}) &\pmod{p} &{if $n$ is even}.
$$ where $n$ is a positive integer and $p$ is prime such that $p>\max(n+1,3)$.

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