Calculating Remainders

What is the remainder when 7 1 2018 6 2 2017 71^{2018} - 62^{2017} is divided by 9 9 ?

2 7 0 4

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2 solutions

Otto Bretscher
Dec 13, 2018

7 1 2018 6 2 2017 ( 1 ) 2018 ( 1 ) 2017 = 2 ( m o d 9 ) 71^{2018} - 62^{2017}\equiv (-1)^{2018}-(-1)^{2017}=\boxed{2} \pmod{9}

Naren Bhandari
Dec 14, 2018

Since A = ( 72 1 ) 2018 ( 63 1 ) 2017 A= (72-1)^{2018} -(63-1)^{2017} Thus, A m o d ( 9 ) = 1 ( 1 ) 2017 = 2 A\mod(9) = 1-(-1)^{2017} =2 .

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