perplexus.info :: Just Math : Integer solutions of cubic

Integer solutions of cubic (Posted on 2025-05-04)

Find all integers m for which the equation

x³ - mx² + mx - (m² + 1) = 0

has an integer solution.

No Solution Yet Submitted by Danish Ahmed Khan

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re: Possible Solution

Comment 2 of 2 |

(In reply to Possible Solution by broll)

Just for solution completeness, if (x-m)(m+x^2)=1,

then it is also possible that (x-m) = (m+x^2) = -1

Then m = x + 1

so (x+1+x^2) = -1,

so x^2 + x +2 = 0

This has no real solutions, so Broll's are the only solutions,

Posted by Steve Herman on 2025-05-04 17:35:01

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