MathDB

4

Part of 2020 China Girls Math Olympiad

Problems(1)

Gcd of factorial minus 1

Source: CGMO 2020 Day1 P4

8/10/2020
Let p,qp,q be primes, where p>qp>q. Define t=gcd⁡(p!−1,q!−1)t=\gcd(p!-1,q!-1). Prove that t≤pp3t\le p^{\frac{p}{3}}.
number theorygreatest common divisorfactorialCGMO