Question

Find the remainder when 21^875 is divided by 17

Answer 1

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Answer 2

The answer would be 13.

1)  Consider this equation

21=4mod(17)

2)Raising the power by 875  

21^875=(4)^875* mod(17)

3) The 875 can be broken into 874 + 1  and 874 can be further broken as 2*437

(4^2)^437×4=(−1×4)mod(17)

4) 4^2 = 16

(16)^437×4=(−1×4)mod(17)

5) Equating the above equation

(4)875=(−4)mod(17)

6)

Therefore,⇒21^875=(17−4)mod(17)

21^875=13mod(17)

7) Hence, the remainder is 13

R(218^75/17)=13