#Olympiad Math - Diophantine Equations | Math Avenue : Learn Math By Examples
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The Uncracked Problem With 33: Mathematician Solves 64-year-old ‘Diophantine Puzzle’
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3.2.10 In this question, we prove the Theorem on integer solutions to linear equations. Let a, b, c be integers. Suppose that (xo, Yo) and (x1, Y1) are two integer solutions to the linear Diophantine equation ax by = 0.(a) Show that (Xo X1, Yo Y1) satisfies the equation ax by = 0.(b) Suppose that gcd(a, b) = d. Prove that gcd(3, 4) = 1. (Use Question 2.9)(c) Find all integer solutions (x, y) to ax by = 0 (Don't use the Theorem, it's what you're trying to prove! Think about part (b) and
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