A Binomial Coefficient Congruence Modulo Prime Powers
نویسندگان
چکیده
منابع مشابه
Binomial Character Sums modulo Prime Powers
We show that the binomial and related multiplicative character sums p ∑ x=1 (x,p)=1 χ(x(Ax +B)), p ∑ x=1 χ1(x)χ2(Ax k +B), have a simple evaluation for large enough m (for m ≥ 2 if p ABk).
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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 f ∑ k≡r (mod pα) (n k ) (−1)f ( k − r pα ) ≡ 0 ( mod p ∑∞ i=α n/p i ) (motivated by a conjecture arising from algebraic topology) and obtain the following vast generalization of Lucas’ theorem: If α is greater than one, and l, s, t are nonnegative integers with s, t < p, then 1 ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1993
ISSN: 0022-314X
DOI: 10.1006/jnth.1993.1002