I really don't know how to start this problem. The problem should be related to factoring the equation to derive an answer, but I don't know how.
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7$m^5+m+1=(m^2+m+1)(m^3-m^2+1).$ And for your case one of these factors must be $ 1,$ which won't be difficult to solve. – Bumblebee Jun 10 '22 at 03:46
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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Jun 10 '22 at 03:47
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4@Bumblebee or $-1.$ – Thomas Andrews Jun 10 '22 at 04:26
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Same methods in the linked dupe work, see esp. [here](https://math.stackexchange.com/a/2012356/242). – Bill Dubuque Jun 19 '22 at 09:11