MathDB
2022 Algebra/NT #10

Source:

March 11, 2022
number theory

Problem Statement

Compute the smallest positive integer nn for which there are at least two odd primes pp such that ∑k=1n(−1)vp(k!)<0\sum_{k=1}^{n} (-1)^{v_p(k!)} < 0. Note: for a prime pp and a positive integer mm, vp(m)v_p(m) is the exponent of the largest power of pp that divides mm; for example, v3(18)=2v_3(18) = 2.
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