MathDB

8

Part of 2019 Canadian Mathematical Olympiad Qualification

Problems(1)

for every prime p there is an integer k for which p divides k and k is a peak

Source: Canada Repêchage 2019/8 CMOQR

3/2/2020
For t≥2t \ge 2, defi ne S(t)S(t) as the number of times tt divides into t!t!. We say that a positive integer tt is a peak if S(t)>S(u)S(t) > S(u) for all values of u<tu < t. Prove or disprove the following statement: For every prime pp, there is an integer kk for which pp divides kk and kk is a peak.
number theorydividesinequalities