(p2 + 2q)/(q + r), (q2 + 9r)/(r + p), and
(r2 + 3p)/(p + q)
is a positive integer.
Prove that no further triplet is possible in conformity with the given conditions.
Note: Adapted from a problem appearing in a shortlist of Junior Balkan Mathematical Olympiad.
*** Computer program assisted solutions are welcome, but a semi-analytic methodology, that is: hand calculator and p&p, is preferred.
