Solution
= Solution
Let $d=\gcd(c,n)$, and write $c=dc'$, $n=dn'$ with positive <integers> $c',n'$. If an <integer> $e>1$ divided both $c'$ and $n'$, then $de$ would divide both $c$ and $n$, contradicting the maximality of their <greatest common divisor> $d$. Thus \b[$\gcd(c',n')=1$]. Equivalently, <Bézout's identity> for $c,n$ can be divided by $d$ to express $1$ as an <integer> combination of $c',n'$.