Getting Quadratic With Two Digits (Posted on 2007-09-07)

(A) x is a two digit positive integer with no leading zero and d is the product of its digits. Determine all possible values of x such that x^{2} – 10x – d is a perfect square.

(B) p is a two digit positive integer with no leading zero and c is the product of its digits. Determine all possible values of p such that p^{2} – 12p – c is a perfect square.