What will be the remainder when 23⁸ - 29 is divided by 22?

Question

Question

This question was previously asked in

CRPF Constable Technical Tradesman Official Paper (Held On: 01 July, 2023 Shift 2)

Answer 1

Given:

We need to find the remainder when 23⁸ - 29 is divided by 22.

Formula used:

Using modular arithmetic, we calculate:

(aⁿ - b) mod m

Calculation:

23 ≡ 1 (mod 22), since 23 leaves a remainder of 1 when divided by 22.

⇒ 23⁸ ≡ 1⁸ (mod 22)

⇒ 23⁸ ≡ 1 (mod 22)

Now, computing (1 - 29) mod 22:

⇒ (1 - 29) ≡ -28 (mod 22)

⇒ -28 ≡ 16 (mod 22) (since -28 + 22 = -6 and -6 + 22 = 16)

∴ The remainder is 16.

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