The distribution of the binomial coe cients modulo pRichard

Content Provider	Semantic Scholar
Author	Wilf, Herbert S.
Abstract	If p is a prime, a is a primitive root modulo p, and n is a positive integer, let r i (n) be the number of k such that 0 k n and ? n k a i modulo p, and let R n (x) = P p?2 i=0 r i (n)x i be their generating function. We show that R n (x) Q p?1 j=1 R j (x) t j modulo (x p?1 ?1), where t j is the number of appearances of the digit j in the p-ary expansion of n. The proof uses the fact that a certain mapping of p-ary digit strings to polynomials modulo (x p?1 ? 1) is a homomorphism. We use this result to study how the values of the binomial coeecients sit in the quadratic residues modulo p.
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Alternate Webpage(s)	http://www.math.upenn.edu/~wilf/website/residues.ps
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article