I want to find all the integer values of $c$ for which $\frac{c^6-3}{c^2+2}$ is an integer.
By inspection $\pm 3$ is a solution. However, is there any systematic way to find all the solutions?
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1Hint : $c^2+2\mid c^6+8$ implies $c^2+2\mid 11$ – Peter Feb 21 '22 at 08:59
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@Peter thanks it solved the problem – Feb 21 '22 at 09:03