Problem 3
Determine all pairs (p,n), where p is a prime number and n is a positive integer, for which (n^p+1)/(p^n+1) is an integer.
Step 2 of 7: Handle p=2
Detailed analysis
For p=2, 2^n>n^2 for n≥5, so only n=1,2,3,4 remain. Substitution shows exactly n=2 and n=4 satisfy the divisibility condition.