A Binomial Sum Related to Wolstenholme’s Theorem
نویسندگان
چکیده
A certain alternating sum u(n) of n + 1 products of two binomial coefficients has a property similar to Wolstenholme’s theorem, namely u(p) ≡ −1 (mod p3) for all primes p ≥ 5. However, this congruence also holds for certain composite integers p which appear to always have exactly two prime divisors, one of which is always 2 or 5. This phenomenon will be partly explained and the composites in question will be characterized. We also study the sequence u(n) in greater detail, especially its growth and its sign distribution.
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تاریخ انتشار 2009