Thread: decimal expansion of 7^999,999

I'm trying to figure out how to solve this problem. I have flipped thru my notes and I can't find an example of how to do this problem.

Find the decimal expansion of {7}^{999999}.
Thanks for the help.

Originally Posted by drounds67

I'm trying to figure out how to solve this problem. I have flipped thru my notes and I can't find an example of how to do this problem.

Find the decimal expansion of {7}^{999999}.
Thanks for the help.

i don't know how many digits does this have. i didn't calculate. Use logarithms for that.
But i can tell you the last 7 numbers in the decimal expansion.
use euler's generalization of fermat's little theorem to get
this implies why?
the above two give .
let
so
the inverse of 7 wrt 10^7 is 2857143(you can go to wolframalpha for this or can do some long time computing yourself )
so,
hence the last 7 digits of are

i know that 7 is nothing compared to the number of digits in 7^{999999} but still...

Hello, drounds67!

What is the original wording of the problem?
As stated, the problem is really difficult to answer.

. . . . . . . . . . . . . .


Hence: .

. .







So what exactly did they ask for?