RO-TST 1992 Problem 7

Let $(a_{n})_{n\geq 1}$ and $(b_{n})_{n\geq 1}$ be the sequence of positive integers defined by $a_{n+1}=na_{n}+1$ and $b_{n+1}=nb_{n}-1$ for $n\geq 1$ . Show that the two sequence cannot have infinitely many common terms.

Laurentiu Panaitopol