Abstract
Finding congruences between different arithmetic objects has always been a challenging task. From Kummer we have beautiful relations between the Bernoulli numbers Bn which have a wide range of important applications to different areas of mathematics. If n,m are even positive integers and p is a prime with (p−1) n and n ≡ m (mod p−1), then Bn n ≡ Bm m (mod p). This leads directly to congruences for the Riemann zeta function ζ(s)
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