A number theory problem by Dev Sharma

Number Theory Level 3

Find the remainder when 2^39 is divided by 39.


The answer is 8.

Dev Sharma by Dev Sharma , 20, India

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2 solutions

Dev Sharma
Aug 19, 2015

Using Euler totient function, E(39) = 24

2^24 = 1 mod39

2^10 = 10 mod39

2^34 = 10 mod39

Also, 2^5 = 32 mod39

Thus 2^39 = 8 mod39

1 Helpful 0 Interesting 0 Brilliant 0 Confused

2^9=5 mod 39

2^36=(5^4) mod 39=1 mod 39

2^39=(5^3) mod 39=8 mod 39

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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