On the parity of exponents in the standard factorization of n!

JOURNAL OF NUMBER THEORY

卷:100

Article; Proceedings Paper

Chen, YG

关键词: Erdos problems;    parity;    prime factorization;    factorials;   

DOI  :  10.1016/S0022-314X(03)00013-1

来源: Elsevier

【 摘 要 】

Let p(1), p(2),... be the sequence of all primes in ascending order. The following result is proved: for any given positive integer k and any given epsiloni is an element of {0, 1} (i = 1, 2,..., k), there exist infinitely many positive integers n with e(1) (n!) equivalent to epsilon(1) (mod 2), e(2) (n!) equivalent to epsilon(2) (mod 2),..., e(k) (n!) equivalent to epsilon(k) (mod 2), where e(i)(n!) denotes the exponent of the prime pi in the standard factorization of positive integer n!. In 1997 Berend proved a conjecture of Erdos and Graham, that is, the conclusion with all epsilon(i) = 0. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

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