alleryRemainder when 7^100 is divided by 5:
A2
B1 (7 ≡ 2 mod 5; 2^100 = (2^4)^25 = 16^25 ≡ 1^25 = 1 mod 5)
C0
D4
Answer & Solution
Correct answer: B. 1 (7 ≡ 2 mod 5; 2^100 = (2^4)^25 = 16^25 ≡ 1^25 = 1 mod 5)
7 ≡ 2 (mod 5). 7^100 ≡ 2^100 (mod 5).
By Fermat's little theorem, 2^4 ≡ 1 (mod 5).
2^100 = (2^4)^25 ≡ 1^25 = 1 (mod 5). Remainder = 1.
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