Problem $1.$ Simplify the following using modular exponentiation. You really need

to be fluent by the time we hit crytography.

$($a$)17463$ mod $1104.$

$($b$)6090$ mod $91.$

$($c$)67263156919$ mod $991.($Hint: begin by simplifying the problem using Fermat$$s

theorem. Remember to check that its hypotheses are satisfied.$)$

$($d$)21107$ mod $1109.($Hint: explain why this is the same as finding the multi$-$

plicative inverse of $2,$ and then find it by the method we learned. $($Or do it in your

head! inverting $2$ modulo an odd number is easy.$)$ Easier or harder than doing the

exponentiation?$)$