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Number Theory Level 2

find the remainder when $36^{{36}^{36} }$ is divided by 37.

2 36 7 1 5 35

1 solution

Maggie Miller
Jul 30, 2015

Note $36^{36}$ is even and $36\equiv -1\pmod{37}$ . Then $36^{36^{36}}\equiv (-1)^{36^{36}}\pmod{37}\equiv\boxed{1}\pmod{37}$ .

Very nice and clear solution.the same as of mine.upvoted

abhigyan adarsh - 5 years, 10 months ago