On the parity of exponents in the factorization of n!

[摘要] It is shown that, for any ic, there exist infinitely many positive integers n such that in the prime power factorization of n !, all first k primes appear to even exponents. This answers a question of Erdos and Graham (''Old and New Problems and Results in Combinatorial Number Theory,'' L'Enseignement Mathematique, Imprimerie Kundia, Geneva, 1980). A few generalizations are provided as well. (C) 1997 Academic Press.

[发布日期] 1997-05-01