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Number theory

Source: Iranian TST 2018, second exam, day1, problem 3

April 15, 2018
number theory

Problem Statement

Let a1,a2,a3,⋯a_1,a_2,a_3,\cdots be an infinite sequence of distinct integers. Prove that there are infinitely many primes pp that distinct positive integers i,j,ki,j,k can be found such that p∣aiajak−1p\mid a_ia_ja_k-1.
Proposed by Mohsen Jamali
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