find the least nonnegative integer in the congruence class [ 59^110]14?

Answer 1

Let n=59^110 (mod 14)
then n=59^110=1^110=1 (mod 2) and n=3^110 (mod 7)

3^110=(3^18)^6•3^2=9=2 (mod 7)

Thus n=1=-5 (mod 2) and n=2=-5 (mod 7)

Thus n=-5=9 (mod 14)

n=9 is the smallest such positive number.

Answer 2

i say 0