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a^k+n are all composite numbers

Source: China second round 2018 (B) Q4

June 22, 2019
number theory

Problem Statement

Prove that for any integer a≥2a \ge 2 and positive integer n,n, there exist positive integer kk such that ak+1,ak+2,…,ak+na^k+1,a^k+2,\ldots,a^k+n are all composite numbers.
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