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ad - bc = + - 1 if ax + by = m and cx + dy = n

Source: Eotvos 1942 p2

September 10, 2024
number theorysystem of equationsSystemdiophantine

Problem Statement

Let a,b,ca, b, c and dd be integers such that for all integers m and n, there exist integers xx and yy such that ax+by=max + by = m, and cx+dy=ncx + dy = n. Prove that ad−bc=±1ad - bc = \pm 1.
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