2001 IMO Shortlist Problems/N5
Let be positive integers and suppose that
Prove that is not prime.
Equality is equivalent to .
Let be the quadrilateral with , , , , , and . Such a quadrilateral exists by and the Law of Cosines.
By Strong Form of Ptolemy's Theorem, we find that;
and by rearrangement inequality;
Assume is a prime, since is an integer must be an integer but this is false since and . Thus can not be a prime.