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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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Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(2): A way not to do it. Comment 4 of 4 |
(In reply to re: A way not to do it. by Jer)

After further playing around, I reached the rather concise:

2b^2+4ab = x^4-y^2

but I still don't see an analytic path forward from that.

Edited on June 14, 2016, 5:10 am
  Posted by broll on 2016-06-14 05:10:32

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