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Roots on Unit Circle Equation

2550MasterPolynomialsComplex NumbersCombinatorics

74th NMO Shortlisted Problems

Let $k \ge 2$ be a given positive integer. Determine the number of pairs $(m, n)$ of positive integers, with $m, n < 2^k$, such that the equation $z^{2^k} - z^m - z^n = 1$ has at least one solution with modulus $1$. Bogdan Blaga
0 students attempted0% solvedRating 2550

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