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find the number of solutions of a flool function equation

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April 10, 2011
functionalgebrafloor functionalgebra unsolved

Problem Statement

Let NN be a natural number. Find (with prove) the number of solutions in the segment [1,N][1,N] of the equation x2−[x2]=(x−[x])2x^2-[x^2]=(x-[x])^2, where [x][x] means the floor function of xx.
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