Problem Statement

Find the last   40   decimal digits of

a

b

{\displaystyle a^{b}}

,   where

A computer is too slow to find the entire value of

a

b

{\displaystyle a^{b}}

. Instead, the program must use a fast algorithm for modular exponentiation:

a

b

mod

m

{\displaystyle a^{b}\mod m}

. The algorithm must work for any integers

a , b , m

{\displaystyle a,b,m}

,     where

b ≥ 0

{\displaystyle b\geq 0}

and

m

0

{\displaystyle m>0}

.

Let's start with the solution:

a := 2988348162058574136915891421498819466320163312926952423791023078876139:
b := 2351399303373464486466122544523690094744975233415544072992656881240319:
a &^ b mod 10^40;