Remainder[( 77^99)/101]=?

Question

Answer 1

Euler of 101 = 101*(1-1/101) = 100
So, 77^100 mod 101 = 1
Let 77^99 mod 101 = k
77k mod 101 = 1
77k = 101t + 1
=> k = (101t + 1)/77
For t = 16, we get k = 21

Remainder = 21

Answer 2

Euler of 101 = 101*(1-1/101) = 100
So, 77^100 mod 101 = 1
Let 77^99 mod 101 = k
77k mod 101 = 1
77k = 101t + 1
=> k = (101t + 1)/77
For t = 16, we get k = 21

Remainder = 21

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Remainder[( 77^99)/101]=?