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Sum Two Squares (Posted on 2007-11-02)

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.

Submitted by K Sengupta

Rating: 3.5000 (2 votes)

Solution: (Hide)

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

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Solution extra "trivial" solution	Daniel	2007-11-02 18:03:46
Solution	Dej Mar	2007-11-02 10:19:07

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