Find the shortest method!

Number Theory Level 4

$\Large 32^{32^{32}} \bmod 7 = \, ?$

3 6 7 1 2 4 5 0

1 solution

Ashwin K
Feb 2, 2016

This is a good question.

Find the remainder when 32 divided by 7 which is 4.

We get 4^32^32

Then, when we multiply 2 4's, we get 16 and divided by 7 gives remainder as 2 and again take one 2 from power to make it 4.

After the above step, we have 4^32^30

By repeating the steps we end up with 4^32^0 which means 4^1=4

Yes it is right. Try using binomial theorem for an alternate way.

Aditya Kumar - 5 years, 4 months ago