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Putnam 1968 A2

Source: Putnam 1968

February 19, 2022
Putnamapproximation

Problem Statement

Given integers a,b,c,d,m,na,b,c,d,m,n such that ad−bc≠0ad-bc\ne 0 and any real ε>0\varepsilon >0, show that one can find rational numbers x,yx,y such that 0<∣ax+by−m∣<ε0<|ax+by-m|<\varepsilon and 0<∣cx+dy−n∣<ε0<|cx+dy-n|<\varepsilon.
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