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Sum Two Squares (Posted on 2007-11-02) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

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re: Solution extra "trivial" solution Comment 2 of 2 |
(In reply to Solution by Dej Mar)

(2,1,1) works on a technicality because qr=1 and since there are no primes less than or equal to sqrt(2) then we can truthfully say that qr/s is an integer for all prime s<=sqrt(p) with p=q^2+r^2
  Posted by Daniel on 2007-11-02 18:03:46

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