QA – Placement Quizzes | SP Contest 2 | Question 2

What will be the remainder when 7¹⁰⁰ is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3

Answer: (B)
Explanation: This is a basic question of Chinese remainder theorem(CRT):

We can write 7¹⁰⁰ as (7⁴)²⁵.

Now, 7⁴ = 2401 when we divide it by 5 then 1 will be the remainder.

Now, 7¹⁰⁰ as (7⁴)²⁵ = (2401)²⁵ mod 5 = 1²⁵ mod 5 = 1.

Therefore, (7¹⁰⁰ % 5) = 1.
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