Determine all possible triplets of positive integers (p, q, r) satisfying p = q
^{2} + r
^{2} 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 = 1^{2} + 2^{2}; 1 <= 2; gcd(1,2) = 1
1*2/2 = 1; 2 <= SQRT(5) ~=2.236
13 = 2^{2} + 3^{2}; 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 20071102 10:19:07 