Algebra · Polynomial identities · Roots of unity · Exponents
Problem 3, 1995
If \(a^{2} + a + 1 = 0\), what is the value of \[ a^{1995} + \frac{1}{a^{1995}} \, ? \]
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Serbian Municipal Competition 1995, high school grade I, problem 3. Organized by the Mathematical Society of Serbia (DMS).