#4 (2016 Iran 3rd N1)
感想
なかなか面白い問題. 主張が強くて面白い.
所要時間60分, 難易度5
原文
Let \(p,q\) be prime numbers (\(q\) is odd). Prove that there exists an integer \(x\) such that:
\[q |(x+1)^p-x^p\]If and only if \[q \equiv 1 \pmod p .\]
なかなか面白い問題. 主張が強くて面白い.
所要時間60分, 難易度5
Let \(p,q\) be prime numbers (\(q\) is odd). Prove that there exists an integer \(x\) such that:
\[q |(x+1)^p-x^p\]If and only if \[q \equiv 1 \pmod p .\]