On the parity of exponents in the factorization of n!

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16 Scopus citations


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.

Original languageEnglish
Pages (from-to)13-19
Number of pages7
JournalJournal of Number Theory
Issue number1
StatePublished - 1 Jan 1997

ASJC Scopus subject areas

  • Algebra and Number Theory


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