A ug 2 00 5 Preprint ( August 4 , 2005 ) A COMBINATORIAL CONGRUENCE ON POLYNOMIALS
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چکیده
Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f (x) ∈ Z[x]. We establish the congruence p deg f k≡r (mod p α) n k (−1) k f k − r p α ≡ 0 mod p ∞ i=α ⌊n/p i ⌋. This result is a vast generalization of a conjecture arising from algebraic topology. An application to Bernoulli polynomials is also given.
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تاریخ انتشار 2005