Question
Find the remainder when (5)100 is divided by
7Solution
ATQ, By Fermat's Little Theorem, since 7 is prime, we have: 56 = 1(mod 7) Thus, 5100 = 5(6×16+4) = (56)16 × 54 = 116 × 54 = 54 (mod 7) 52 = 25 = 4 (mod 7) 54 = (52)2 = 16 = 2 (mod 7) Thus, the remainder is 2 .
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