Determine all pairs $ (n,p)$ of positive integers, where $ p$ is prime, such that $ 3^p-np=n+p$.
Problem
Source: Indonesia IMO 2007 TST, Stage 2, Test 5, Problem 4
Tags: number theory, greatest common divisor, number theory proposed
Source: Indonesia IMO 2007 TST, Stage 2, Test 5, Problem 4
Tags: number theory, greatest common divisor, number theory proposed
Determine all pairs $ (n,p)$ of positive integers, where $ p$ is prime, such that $ 3^p-np=n+p$.