# How did Euler solve the 4-whole-numbers-adding-up-to-a-perfect-square problem?

So I was watching a video on Leonhard Euler about how he amazingly solved so many difficult problems and one of the many problems that he solved was this:

Find four whole numbers, the sum of any two of which add up to a perfect square.

The numbers he found were: $$18530,~~~ 38114,~~~ 45986,~~~ 65570$$

I've searched everywhere on the net but I can't find how he solved this. Does anyone here know how he did it?

Thanks.

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I suspect the first thing to try is to find three whole numbers, the sum of any two of which add up to a perfect square. See if you can find any pattern to the set of such triples. – Thomas Andrews Dec 4 '12 at 21:40