MathDB

3

Part of 2016 JBMO TST - Turkey

Problems(1)

Primes and divisibility

Source: Turkey JBMO TST 2016 P3

5/22/2016
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.
number theoryprime numbers