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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: Possible solution | Comment 3 of 4 |
(In reply to Possible solution by broll)

Broll:


How did you solve (a*(q-p)(q+p))/(q^2-21)=p^2?

Not real clear (or simple) to me.




  Posted by Steve Herman on 2011-01-17 17:18:01
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