That's exponential mod

Number Theory Level 1

3 12435261235173 m o d 2 = ? { 3 }^{ 12435261235173 } mod 2=?


The answer is 1.

Shivamani Patil by shivamani patil , 21, India

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4 solutions

Drop TheProblem
Sep 2, 2014

3=1 mod2. So 1x1x1x1x....x1x1... (12435261235173 times) is equal to 1

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Exactly the same!!:D

Anik Mandal - 6 years, 9 months ago

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Exactly the same!!:D

math man - 6 years, 9 months ago
Sophie Crane
Sep 27, 2014

Any power of an odd number is itself odd.

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Sameer Pai
Oct 23, 2014

It is simple to prove by induction that 3^n-1 = 0 mod 2. Therefore, 3^n = 1 mod 2, so 3^12435261235173 = 1 mod 2

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Ali Rahil
Sep 14, 2014

a^nMODb=(aMODb)^nMODb

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