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max a, such that system : x - 4y = 1, ax + 3y = 1 has an integer solution

Source: 1972 Swedish Mathematical Competition p1

March 26, 2021
diophantinesystem of equationsSystemnumber theory

Problem Statement

Find the largest real number aa such that {x−4y=1ax+3y=1\left\{ \begin{array}{l} x - 4y = 1 \\ ax + 3y = 1\\ \end{array} \right. has an integer solution.
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