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Sum and Ratio Sum (Posted on 2011-01-16) Difficulty: 3 of 5
Determine all possible quadruplets (A, B, P, Q) of positive integers, with P ≤ Q, that satisfy this system of equations:

A + B = 21, and:

A/P2 + B/Q2 = 1

Prove that these are the only quadruplets that exist.

No Solution Yet Submitted by K Sengupta    
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re(2): Possible solution Comment 4 of 4 |
(In reply to re: Possible solution by Steve Herman)

Steve,

I'm afraid that's all the work I did on it (apart from some jottings on equalities of the form w/x^2+y/z^2=1) Once I got to the formula I gave, it seemed obvious that there could only be those answers, so I didn't explore further.


  Posted by broll on 2011-01-18 01:57:24
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