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.

(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