A cube square difference
Do there exist integers m and n such that this holds?
∣ ∣ m 2 − n 3 ∣ ∣ = 5
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1 solution
How do you know that's the only solution?
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I don't. Do you?
That's why I phrased the question the way I did. :-)
By the way, I've been wrestling with another problem. Are there integers m and n such that ∣ m 2 − n 3 ∣ = 6 .
Any idea on how to approach this?
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These are of course Mordell's equations, and there is no solution for either m 2 − n 3 = 6 or m 2 − n 3 = − 6 , as indicated here , (see the two sequences in the "Properties" section). Some solution methods are given here , (note specifically theorems 2.3 and 2.5).
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@Brian Charlesworth – Ah, very interesting... Thanks for pointing this out... Will take a look!
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@Geoff Pilling – If you're interested, have a look at the discussion here .
Yes. One possibility is m = 2 and m = − 1 .
Bonus question : Do there exist integers m and n such that the absolute value equals 6?