On the Parity of Exponents in the Factorization ofn! Original Research Article

It is shown that, for anyk, there exist infinitely many positive integersnsuch that in the prime power factorization ofn!, all firstkprimes appear to even exponents. This answers a question of Erdimages and Graham (“Old and New Problems and Results in Combinatorial Number Theory,” LʹEnseignement Mathématique, Imprimerie Kundia, Geneva, 1980). A few generalizations are provided as well.