Okay so if you are given how would you figure out the last two digits of the munber using mod.

- August 2nd 2009, 11:04 AMdiddledabble[SOLVED] Finding the last two digits of a number raised to a large exponent
Okay so if you are given how would you figure out the last two digits of the munber using mod.

- August 2nd 2009, 11:44 AMrunning-gag
- August 2nd 2009, 11:48 AMdiddledabble
But how do you work through it. I did it for and got 143 but I am not confident on my steps. I don't want anyone to solve my homework. That is why I altered my question to . I just need a good detailed step by step explanation. Thanks

- August 2nd 2009, 01:22 PMo_O
Use Euler's theorem: where

So we know:

Thus:

Now use the property: - August 2nd 2009, 01:52 PMSoroban
Hello, diddledabble!

Quote:

Find the last two digits of: .

. .

The endings form a four-step cycle: .

Since has the third ending: .

- August 4th 2009, 02:28 PMdiddledabble
Soroban,

Your answer was sooo easy to understand. Just what I was looking for.