China Mathematics Olympiads (National Round) 2008 Problem 6
Source:
November 28, 2010
modular arithmeticalgebrapolynomialVietanumber theory unsolvednumber theory
Problem Statement
Find all triples that satisfy
q^{n+2} \equiv 3^{n+2} (\mod p^n) , p^{n+2} \equiv 3^{n+2} (\mod q^n)
where are odd primes and is an positive integer.