Izvorni znanstveni članak
An analog of Wolstenholme’s theorem
Boaz Cohen
; Department of Computer Science, The Academic College of Tel-Aviv, Israel
Sažetak
In this paper we shall prove an analogous version of Wolstenholme's theorem, namely, given a prime number p>=2 and positive integers a,b,m such that p|-m, we shall determine the maximal prime power \(p^e\) which divides the numerator of the fraction \(1/m=1/(m+p^b)+...+1/(m+(p^a-1)p^b\), when written in reduced form, with the exception of one case, where p=2, b=1, m>1 and \(2^a||m-1\). In this exceptional case, a lower bound for e is given.
Ključne riječi
Wolstenholme's Theorem, Bauer's Theorem, Congruences, Primes
Hrčak ID:
303379
URI
Datum izdavanja:
2.6.2023.
Posjeta: 176 *