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no of solutions of x^2 - [x^2] = \left(x - [x]\right)^2 if 1 <= x <=n

Source: 1982 Swedish Mathematical Competition p1

March 28, 2021
floor functionalgebra

Problem Statement

How many solutions does x2−[x2]=(x−[x])2 x^2 - [x^2] = \left(x - [x]\right)^2 have satisfying 1≤x≤n1 \leq x \leq n?
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