Thus, 120 x + 168 y = 24 for some x and y. Let's find the x and y. Proof. . Say we know that there are solutions to $ax+by=\gcd(a,b)$; then if $k$ is an integer, there are obviously solutions to $ax+by=k\gcd(a,b)$. | 1 As $S$ contains only positive integers, $S$ is bounded below by $0$ and therefore $S$ has a smallest element. Furthermore, $\gcd \set {a, b}$ is the smallest positive integer combination of $a$ and $b$. 0 , Then by repeated applications of the Euclidean division algorithm, we have, a=bx1+r1,0
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Articles B