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Solve [x]^5+{x}^5=x^5

Source: Romanian District Olympiad 2012, Grade IX, Problem 1

October 9, 2018
equationsalgebrafractional partInteger PartFloor

Problem Statement

Solve in R \mathbb{R} the equation [x]5+{x}5=x5, [x]^5+\{ x\}^5 =x^5, where [],{} [],\{\} are the integer part, respectively, the fractional part.
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