Is there a technique other than performing Euclid's algorithm in reverse that can elegantly show that if GCD$(a,b) = d$ then there exist integers $x$ and $y$ such that $ax + by = d$?
2026-04-26 08:34:17.1777192457
GCD to Linear Diophantine Equation without Euclid Algorithm
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HINT: Consider the smallest positive integer that can be written as $ax+by$