Remainders are fun

Number Theory Level 3

100 7 2013 1007^{2013} is divided by 2014 2014 , what will be the remainder?

1 1007 2 2013

Raghav Mehta by Raghav Mehta , 30, India

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2 solutions

Rishabh Jain
Jul 19, 2014

actually this is a part of this question

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Hemang Sarkar
Jul 18, 2014

1007^2013 be x mod(2014) (2014-1007)^2013 is x mod(2014) or, -1007^2013 is x mod(2014) adding the first and the third, 2x is 0 mod(2014). x is 1007.

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