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{x [x] } = 0.5 (V Soros Olympiad 1998-99 Round 1 9.6)

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May 25, 2024
algebrafractional part

Problem Statement

How many solutions satisfying the condition 1<x<51 < x < 5 does the equation {x[x]}=0.5\{x[x]\} = 0.5 have?
(Here [x][x] is the integer part of the number xx, {x}=xāˆ’[x]\{x\} = x - [x] is the fractional part of the number xx.)
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