Evalute in mod 77.

I know that , but how should I continue? Thanks.

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- Mar 26th 2008, 12:16 PMtttcomraderModule 77
Evalute in mod 77.

I know that , but how should I continue? Thanks. - Mar 26th 2008, 12:32 PMtopsquark
- Mar 26th 2008, 01:49 PMMoo
Hello,

I guess you wanted to use Fermat's little theorem. Unfortunately, this only works if 77 is a prime number.

Otherwise, you can use Euler's theorem which states that :

With the Euler's totient function, defined as :

(p designing prime numbers)

(the first one can be a deduction of this one)

(with q a prime number)

As 77 is 11x7,

=> - Mar 26th 2008, 02:22 PMtttcomrader
I actually got to this point with Euler, but then I'm stuck here.

- Mar 26th 2008, 02:30 PMMoo
Well,

Division of 100.000 by 60.

i'll say that 100 is 60x16+40

So 100.000 is 60x16000+40.000

So you can throw off this term...

There is 40.000 remaining : find the remain of 40.000 in the division by 60 (i've shown steps above, because i'm too lazy to take a calculator :D)