ore generally, let g $=$ gcd$($a$,$ b$)$ and let $($u$0,$ v$0)$ be a solution in integers to

au $+$ bv $=$ g$.$ Prove that every other solution has the form u $=$ u$0+$ kb$/$g and

v $=$ v$0$ ka$/$g for some integer k$.($This is the second part of Theorem $1\mathrm{.}11.)$