For positive integer n, note Sn=12024+22024+⋯+n2024. Prove that there exists infinitely many positive integers n, such that Sn isn’t divisible by 1865 but Sn+1 is divisible by 1865
Source: 2024 CWMO P1
Tags: number theory
For positive integer n, note Sn=12024+22024+⋯+n2024. Prove that there exists infinitely many positive integers n, such that Sn isn’t divisible by 1865 but Sn+1 is divisible by 1865