1) Show that ifpis prime, is composite fora= 1,2,....,r andpis not a Fermat prime, whereris a positive integer, then has no solution.

2) The arithmetic funtiongis said to be theinverseof the arithmetic functionfiff * g = g * f = i. Show that the arithmetic functionfhas aninverseif and only if f(1) does not equal 0. Show that iffhas an inverse it is unique.

(Hint: When f(1) is not equal to 0, find the inverse offby calculating recursively, using the fact that i(n) = summation .)