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On the Parity of Exponents in the Prime Factorization of Factorials

✍ Scribed by J.W. Sander

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 126 KB
Volume: 90
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2668

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✦ Synopsis

In 1997 Berend proved a conjecture of Erdo s and Graham by showing that for every positive integer r there are infinitely many positive integers n with the property that

where p(1)=2, p(2)=3, p(3)=5, ... is the sequence of primes in ascending order, and e p (m) denotes the order of the prime p in the prime factorization of the positive integer m. This article presents conjectures and results for the more complicated situation where an arbitrary pattern of residues modulo 2 is given.

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