PUMaC 2010 · 代数（B 组） · 第 2 题
PUMaC 2010 — Algebra (Division B) — Problem 2
题目详情
- Let p ( x ) = x + x + 1. Find the fourth smallest prime q such that p ( n ) is divisble by q for some integer n . √ √ √ √ 1 5 5 5 5 2 2
解析
- Let p ( x ) = x + x + 1. Find the fourth smallest prime q such that p ( x ) has a root mod q . Solution: 19. One can check that there are roots mod 3, 7, 13, and 19, and no others for smaller primes. √ √ √ √ 5 5 5 5 1 2 2 √