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variants of this functions
BernoulliB






Mathematica Notation

Traditional Notation









Integer Functions > BernoulliB[n] > Other identities > Congruence properties





http://functions.wolfram.com/04.13.32.0003.01









  


  










Input Form





Mod[((1 - p^(n - 1))/n) BernoulliB[n], p^e] == (r^n/r^(n - 1)) ((r^EulerPhi[p^e] - 1)/p^e) - Sum[r^(k (n - 1)) Floor[r^k/p^e], {k, 1, EulerPhi[p^e]}] /; Element[p, Primes] && p >= 5 && Element[n, Integers] && n > 0 && NotElement[(p - 1)/n, Integers] && Element[e, Integers] && e >= 1 && Sort[Mod[r^Range[0, p^e - 2], p^e]] == Range[p^e - 1]










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18





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