Problem #PRU-116558

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

13–15 3.0

Problem

The nonzero numbers $a$ , $b$ , $c$ are such that every two of the three equations $a x^{11} + b x^{4} + c = 0$ , $b x^{11} + c x^{4} + a = 0$ , $c x^{11} + a x^{4} + b = 0$ have a common root. Prove that all three equations have a common root.

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