perplexus.info :: Just Math : Integral Roots

Integral Roots (Posted on 2022-04-01)

Show that there are infinitely many pairs of nonzero coprime integers a,b such that both quadratics x^2+ax+b=0 and x^2+2ax+b=0 have integral roots.

No Solution Yet Submitted by Brian Smith

Rating: 5.0000 (1 votes)

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re(2): Different sort of solution

| Comment 4 of 5 |

Nope my mistake. I forgot a,b have to be coprime in all pairs.

I thought it seemed too easy. But of course, once you double them they are no longer coprime.

Posted by Jer on 2022-04-02 08:22:23

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