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A computer which generates integers from reals

Source: Greek National Mathematical Olympiad 2008 - P1

November 17, 2011
algebra unsolvedalgebra

Problem Statement

A computer generates all pairs of real numbers x,yāˆˆ(0,1)x, y \in (0, 1) for which the numbers a=x+mya = x+my and b=y+mxb = y+mx are both integers, where mm is a given positive integer. Finding one such pair (x,y)(x, y) takes 55 seconds. Find mm if the computer needs 595595 seconds to find all possible ordered pairs (x,y)(x, y).
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