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Linear and Quadratic Square (Posted on 2015-03-15) Difficulty: 3 of 5
Each of A and B is a positive integer with gcd(A,B) =1 such that each of
A2 + 2*B2 and A + 2*B is a perfect square.

What is the smallest value of A + 2*B for which this is possible? Determine the next two smallest values of A+2*B that satisfy the given conditions.

No Solution Yet Submitted by K Sengupta    
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re: A way not to do it. | Comment 3 of 4 |
(In reply to A way not to do it. by broll)

Would it help to ignore the directive that GCD(A,B)=1?


I figured the reason it was there was to preclude solutions like (4,48) which is (2^2)*(1,12) but it also rules out the otherwise valid (5,10) whose reduction doesn't work.

  Posted by Jer on 2015-03-16 11:51:33
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