This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2024 USAJMO, 3
Let $a(n)$ be the sequence defined by $a(1)=2$ and $a(n+1)=(a(n))^{n+1}-1$ for each integer $n\geq 1$. Suppose that $p>2$ is a prime and $k$ is a positive integer. Prove that some term of the sequence $a(n)$ is divisible by $p^k$. [i]Proposed by John Berman[/i]
awesomeness_in_a_bun Bézout's identity Chinese remainder theorem Euler's theorem Fermat's little theorem mathematical induction modular arithmetic number theory p-adic valuation parity sequences