Chapter 4.1, Problem 38E

Find each of these values.

a) $\left({\text{19}}^{\text{2}}\text{mod 41}\right) \text{mod 9}$

b) ${\left({\text{32}}^{\text{3}}\text{mod 13}\right)}^{\text{2}} \text{mod 11}$

c) ${\left({\text{7}}^{\text{2}}\text{mod 23}\right)}^{\text{2}} \text{mod 31}$

d) ${\left({\text{21}}^{\text{2}}\text{mod 15}\right)}^{\text{3}}\text{mod 22}$