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We study the solvability of the congruence xⁿ≡ -aⁿm, where n,m₊, a, and (a,m)=1. Our motivation arises from computer experiments concerning a geometric property of the roots of the congruence xⁿ+yⁿ≡ 0p, where n₊ and p. We encounter several OEIS sequences. We also make new observations on some of them.
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Merikoski et al. (2024) studied this question.
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