perplexus.info :: Just Math : List of pairs

List of pairs (Posted on 2015-12-04)

There are infinitely many ordered pairs (m,n) of positive integers for which
m + (m+1) + (m+2) + ... (n-1) + n = mn.

List the first five pairs ordered by values of m.

No Solution Yet Submitted by Ady TZIDON

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re: computer solution -- first eight pairs

| Comment 2 of 3 |

That's about as far as I got: searching quadratic formulas for m that give and integer.

m is given by https://oeis.org/A011900

n is given by https://oeis.org/A001109

each note a recursion relation. I'm trying to prove it.

Posted by Jer on 2015-12-04 12:50:00

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