Determine all possible triplets of positive integers (p, q, r) satisfying p = q² + r² with q ≤ r such that gcd (q, r) = 1 and qr/s is a positive integer for every prime s ≤ √p

Note: gcd denotes the greatest common divisor.

(5,1,2) and (13,2,3).

5 = 1² + 2²;   1 <= 2;   gcd(1,2) = 1
1*2/2 = 1;   2 <= SQRT(5)  ~=2.236

13 = 2² + 3²;   2 <= 3;   gcd(2,3) = 1
2*3/2 = 3;   2 <= SQRT(13)  ~=3.606
2*3/3 = 2;   3 <= SQRT(13)  ~=3.606

Edited on November 2, 2007, 10:21 am

Posted by Dej Mar on 2007-11-02 10:19:07