MathDB

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Part of 2024 China Western Mathematical Olympiad

Problems(1)

Sum of squares in 1865

Source: 2024 CWMO P1

8/6/2024
For positive integer nn, note Sn=12024+22024+⋯+n2024S_n=1^{2024}+2^{2024}+ \cdots +n^{2024}. Prove that there exists infinitely many positive integers nn, such that SnS_n isn’t divisible by 18651865 but Sn+1S_{n+1} is divisible by 18651865
number theory