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2x2 system, <19x>=, <96y>=x (II Soros Olympiad 1997-98 R3 10.7)

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June 6, 2024
algebrasystem of equationsnumber theory

Problem Statement

Let us denote by <a><a> the distance from aa to the nearest integer. (For example, <1,2>=0.2<1,2> = 0.2, <3>=2−3<\sqrt3> = 2-\sqrt3) How many solutions does the system of equations have {<19x>=y<96y>=x   ?\begin{cases} <19x>=y \\ <96y>=x \end{cases} \,\,\, ?
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