lean_workbook_plus_73662

Let $a, b$ , and $c$ be positive integers such that $gcd(a, b) = 1$ . Sequence $\{u_k\}$ , is given such that $u_0 = 0$ , $u_1 = 1$ , and $u_{k+2} = au_{k+1} + bu_k$ for all $k \ge 0$ . Let $m$ be the least positive integer such that $c | u_m$ and $n$ be an arbitrary positive integer such that $c | u_n$ . Show that $m | n$ .