Daniel Berend

It is shown that, for any k, 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 Erdös and Graham ("Old and New Problems and Results in Combinatorial Number Theory," L'Enseignement Mathématique, Imprimerie Kundia, Geneva, 1980). A few generalizations are provided as well.