Modular arithematic

Level 1

Find the remainder when 2 33 2^{33} is divided by 17 17 .

9 2 4 15

Prem Chebrolu by Prem Chebrolu , 17, India

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1 solution

Chew-Seong Cheong
Apr 19, 2018

2 33 ≡ 2 4 × 8 + 1 ≡ 2 ( 1 6 8 ) ≡ 2 ( 17 − 1 ) 8 ≡ 2 (mod 17) \large 2^{33} \equiv 2^{4\times 8+1} \equiv 2(16^8) \equiv 2(17-1)^8 \equiv \boxed{2} \text{ (mod 17)}

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