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JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Binomial Theorem

The remainder when

((64)^{(64)})^{(64)}

is divided by 7 is equal to

(A)4
(B)1✓ Correct
(C)3
(D)6

Answer: (B)

Solution

Since

64 = 9 \cdot 7 + 1

, it follows that

64 \equiv 1 (mod 7)

. Then

((64)^{64})^{64} = 6 4^{6 4^{2}} \equiv 1^{6 4^{2}} \equiv 1 (mod 7)

. The remainder on division by

7

is

1

.

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Single correct option

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