Question
Mathematics Question on Binomial theorem
The remainder when (2021)2023 is divided by 7 is
A
1
B
2
C
5
D
6
Answer
5
Explanation
Solution
The correct answer is (C) : 5
2021 ≡ –2 (mod 7)
⇒ (2021)2023 ≡–(2)2023 (mod 7)
≡ –2(8)674 (mod 7)
≡ –2(1)674 (mod 7)
≡ –2(mod 7)
≡ 5(mod 7)
So when (2021)2023 is divided by 7, remainder is 5.