Funny exponent (Part 1)
Number Theory
Level
2
What are the last seven digits of ?
Note : Ignore initial zeroes of the answer for example if the answer is 0002456 then submit 2456.
The answer is 1.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
9 1 0 6 ≡ ( 1 0 − 1 ) 1 0 6 ≡ ( 1 0 1 0 6 − 1 0 1 0 6 + 5 + ⋯ − 1 0 7 + 1 ) ≡ 1 (mod 1 0 7 )