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Primes and divisibility

Source: Turkey JBMO TST 2016 P3

May 22, 2016
number theoryprime numbers

Problem Statement

Let nn be a positive integer, pp and qq be prime numbers such that pq \mid n^p+2   \text{and}   n+2 \mid n^p+q^p. Prove that there exists a positive integer mm satisfying q∣4m⋅n+2q \mid 4^m \cdot n +2.
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