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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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Possible Solution

| Comment 1 of 2

A strange way of writing (x-m)(m+x^2)=1.

Since both factors taken over the integers must be 1, from the first factor m=(x-1) and substituting,

(x^2+x-1)=1 means x={1,-2} so m={0,-3} with no other integer solutions.

Edited on May 4, 2025, 11:47 am

Posted by broll on 2025-05-04 11:37:14

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