Question

19 has power 92 divide by 92 . find the remainder

Answer 1

when 19^92 is divided by 92, remainder = 77

Answer 2

are you familiar with modular arithmetic?Euler's totient func?fermat's little theorem? I'm going to assume that you're familiar with modular arithmetic.hit me up if you're not

92=23*4

19 is congruent -1 mod 4
19^22 is congruent 1 mod 4
19^22 is congruent 1 mod 23
19^22 is congruent 1 mod 92
19^88 is congruent 1 mod 92
19^92 is congruent 19^4 mod 92 which is congruent 49 mod 92