Question

5.
(a) Find the values of 2^k mod 9 where k = 1, 2, 3, 4, 5, 6, 7, 8, 9.
(b) Find the remainder of 2²⁷¹ when this number is divided by 9.
(c) Find the remainder of 2²⁷¹ when this number is divided by 5.

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THE ANSWERS I GOT YESTERDAY FROM YOUR GUYS WERE WRONG!!!

Answer 1

5)a) If k=1,then 2k=2 and then if we divide it by 9 ,we get the remainder 2. Therefore 2k(mod9)=2,when k=1.

Similarly if k=2, then 2k=4,then if we divide it by 9,we get the remainder 4,Therefore 2k(mod9)=4.

Similarly 2k(mod9)=6,for k=3 and 2k(mod 9)=8,for k=4.

If k=5,then 2k=10,then if we divide it by 9,we get the remainder 1,Therefore 2k(mod9)=1,for k=5.

Similarly 2k(mod 9)=3,5,7,0 for k=6,7,8,9 respectively.

5.b)We have 2271=252×9+3.then if we divide 2271 by 9,we get the remainder 3.

5.c)We have 2271=454×5+1,then if we divide it by 9,we get the remainder 1.