Question Number 114401 by bemath last updated on 19/Sep/20

What is reminder when 4^(29)   divided by 17

Answered by bobhans last updated on 19/Sep/20

because 16 = 4^2 ≡ −1 (mod 17 )  we have 4^4 ≡ (4^2 )^2  ≡ (−1)^2  ≡ 1 (mod 17)  so we obtain 4^(29)  ≡ (4^4 )^7 .4 ≡ 1.4 ≡ 4 (mod 17)  hence the remainder of 4^(29)  upon   division by 17 is equal to 4.

Commented bybemath last updated on 19/Sep/20

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