Abstract
The condition of the problem is equivalent to each of the following statements: the polynomial \((x^3+x^2+x+1)^n+x^n\) is divisible by \(Q(x)=x^4+x^3+x^2+x+1,\) or \((-x^4)^n+x^n\) is divisible by Q(x), or \((-1)^nx^{3n}+1\) is divisible by Q(x).
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Brayman, V., Kukush, A. (2017). 2006. In: Undergraduate Mathematics Competitions (1995–2016). Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-58673-1_34
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DOI: https://doi.org/10.1007/978-3-319-58673-1_34
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