2. Let $Z^+$ be the set of all positive integers.
(a) Use the Euclidean Algorithm to compute gcd(2024, 271) and use that to find
integers $x$ and $y$ so that gcd(2024, 271) = 2024$x$ + 271$y$.
(b) Find integers $u$ and $v$ so that gcd(2024, 271) = 2024$u$ + 271$v$, but $u \neq x$ and
$v \neq y$. Note that $x$ and $y$ are the integers that you found in part (a).
(c) Is it true that: $\forall r, s, t \in Z^+$, gcd($r$, $s$) + gcd($r$, $t$) = gcd($r$, $s + t$)?
Prove your answer.
(d) Is it true that: $\forall m, n \in Z^+$, 2 gcd($m$, $n$) $\leq$ gcd(2$m$, 2$n$)?
Prove your answer.
