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JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Binomial Theorem

Remainder when

6 4^{3 2^{32}}

is divided by 9 is equal to ______.

Answer: 1

Solution

64 = 63 + 1 = 9 \cdot 7 + 1

, so

64 \equiv 1 (mod 9)

.

Raising a congruence to any power preserves it:

6 4^{3 2^{32}} \equiv 1^{3 2^{32}} \equiv 1 (mod 9)

.

The remainder is

1

.

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Integer answer

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