On the parity of exponents in the factorization of n! Academic Article uri icon


  • 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 Erdős 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.

publication date

  • January 1, 1997