Just peeked at the solution; the problem doesn't require PHP after all! Sorry about that.
This is a problem from the first chapter of Miklos Bona's 'A Walk Through Combinatorics': The Pigeon-Hole Principle.
"Find all triples of positive integers a < b < c for which 1/a + 1/b + 1/c = 1 holds."
Any hints showing how this problem can be solved using PHP?