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Guest Message by DevFuse

# (n3+1)/(mn-1)

5 replies to this topic

### #1 plasmid

plasmid

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Posted 07 July 2014 - 07:05 AM

Find all pairs of positive integers m and n such that (n3+1) / (mn-1) is an integer, and prove you've identified them all.

This was a problem I solved back in high school with a proof that could barely fit on one page, written front and back, with small handwriting.

Even looking at it again now, the most elegant proof I can come up with is still pretty complex, but nevertheless sort of neat.

In part, I'm sharing a tricky problem. In part, I'm wondering if there's a more elegant way of solving it than the one I came up with.

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### #2 phil1882

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Posted 07 July 2014 - 03:10 PM

Spoiler for the first half, no proof

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### #3 k-man

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Posted 07 July 2014 - 05:21 PM

Spoiler for more numbers than Phil, but still no proof

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### #4 k-man

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Posted 07 July 2014 - 09:29 PM

I don't have the time to put together a complete proof, but here is how I would go about it...

Spoiler for outline of the proof

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### #5 plasmid

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Posted 08 July 2014 - 04:30 AM

I'll say that that approach would certainly be a different way of going about it than what I did.

Spoiler for Before pursuing that approach much further

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### #6 k-man

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Posted 08 July 2014 - 03:02 PM

So much for a "proof in a hurry" LOL

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