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← JEE Main 2022 · 26 Jun · Shift 1
MathematicsSingle correct+4 / -1Question 5 of 90

JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 5

The remainder when (2021)2023(2021)^{2023} is divided by 7 is :

Choose one option
Answer and worked solution

Official answer: C

Reduce. 2021=7×288+52021=7\times288+5, so we need 52023(mod7)5^{2023}\pmod7.

Cycle. 56≡1(mod7)5^6\equiv1\pmod7 and 2023=6×337+12023=6\times337+1, so 52023≡55^{2023}\equiv5.

(C)