CAN YOU SOLVE THIS ???

Number Theory Level pending

Find the remainder when 2^2005 is divided by 13


The answer is 2.

Vishal S by Vishal S , 21, India

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2 solutions

Anatoliy Razin
Dec 5, 2014

simply 2004 divided by 3 and by 4, i.e. by 12 => 2004th power of 2 is 1 mod 13 (Fermat) or 2005th power is 2

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Could you explain?

Omkar Kulkarni - 6 years, 5 months ago
Riska Mulyani
Dec 5, 2014

2^1=2, 2^2=4,...... 2^12=1 divide 13. So we can write 2^2005=(2^12)^167 x 2^1 =(1)^167 x 2^1 =1 x 2 =2

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