(b). The answer is for m = 9.
and
.
Show that is divisible by 5 for
. By
mathematical induction.
Base: n=1. is divisible by 5.
Induction: Suppose is divisible by 5.
by the above recurrence.
is a multiple of 5 and hence is divisible by 5.
is divisible by 5 by the induction hypothesis. Hence, the resulting
expression is divisible by 5 and so is
.