Question

What is the remainder when 15^400 is divided by 1309?

Answer 1

let us find out the rem (5^400/7) , (5^400/11) and (5^400/17)...1309 equals 7*11*17
so rem (5^400/7)
=(1^400/7)
=1 
similarly 
(5^400/11)
=(256^10/11
=(3^10/11
=(243^2/11
=(1^2/11)
=1
similarly the remainder of the last equation is also 1
so the final answer is equal to one
if you break the larger number into fractions and solve the solution becomes easier
hope this helps you