Question

Find the reminder when 19^{92 is divided by 92}

Answer 1

n^phi(N)=1(modN) for hcf of N,n=1

As phi(92)=44

Thus,19^44=1(mod92),thus 19^88=1(mod92)-1,from simple calculation we see 19^4=49(mod92)-2

Multiplying 1 and 2 we get 19^92=49(mod92)