Divisibility & the Euclidean algorithm

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Bezout's identity guarantees integers $x,y$ with $ax+by=\gcd(a,b)$. For $a=18$ and $b=21$, the extended Euclidean algorithm yields $x=-1$ and $y=1$. Evaluate the Bezout combination $a(-1)+b(1)$, which equals $\gcd(a,b)$.

2. Warm-up

   Bezout's identity guarantees integers $x,y$ with $ax+by=\gcd(a,b)$. For $a=18$ and $b=24$, the extended Euclidean algorithm yields $x=-1$ and $y=1$. Evaluate the Bezout combination $a(-1)+b(1)$, which equals $\gcd(a,b)$.

3. Warm-up

   Bezout's identity guarantees integers $x,y$ with $ax+by=\gcd(a,b)$. For $a=24$ and $b=28$, the extended Euclidean algorithm yields $x=-1$ and $y=1$. Evaluate the Bezout combination $a(-1)+b(1)$, which equals $\gcd(a,b)$.

Problems shown under their original terms: Generated (template, solver-computed).