Abstract
Let ν p (n) be the exponent of p in the prime decomposition of n. We show that for different primes p, q satisfying some mild constraints the integers ν p (n!) and ν q (n!) cannot both be of a rather special form.
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Schlage-Puchta, JC. The exponents in the prime decomposition of factorials. Arch. Math. 107, 603–608 (2016). https://doi.org/10.1007/s00013-016-0963-6
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DOI: https://doi.org/10.1007/s00013-016-0963-6