There are 201 of them.

Number Theory Level 2

What is the remainder when 2 201 2^{201} is divided by 7?


The answer is 1.

Benedict Dimacutac by Benedict Dimacutac , 21, Philippines

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3 solutions

Sidra Tariq
May 3, 2015

2^201=8^67 => when 8÷7, remainder =1 So, when 8^67÷7, remainder=1. :)

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Venkatachalam J
Dec 26, 2016

Relevant wiki: Finding the Last Digit of a Power

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Noel Lo
May 4, 2015

2 201 = ( 2 3 ) 67 = 8 67 2^{201} = (2^3)^{67} = 8^{67}

8 67 = 1 67 ( m o d 7 ) = 1 ( m o d 7 ) 8^{67} = 1^{67} (mod 7) = 1 (mod 7)

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