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Diophantine Equation

Source: 2023 Singapore MO Round 2 Senior Q2 / Junior Q5

June 24, 2023
number theoryDiophantine equation

Problem Statement

Find all positive integers kk such that there exists positive integers a,ba, b such that a2+4=(k2āˆ’4)b2.a^2+4=(k^2-4)b^2.
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