perplexus.info :: Just Math : Linear and Quadratic Square

Linear and Quadratic Square (Posted on 2015-03-15)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

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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