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Hi, I have spme questions about Fermat's little theorem-http://en.wikipedia.org/wiki/Fermat%27s_little_theorem. [Broken]

I need to think about a mathematical algorithm to deal with this theorem- finding pseudo-primes ,aka, Carmichael numbers.

When I'm dealing with huge numbers ,it is very difficult,let's say:

a is 5, n is 200

than getting a number like 5^200 is stupid, and thus I need another method which will prevent the calculation of this number.

anybody can point me to the right direction?

another thing that I noticed is, if we do the test for non prime numbers such as 15

then we get pairs of reminders, I mean:

(7^15)%15 =13

(13^15)%15=7

just something cool(it's not just for these numbers!! )

Thanks in advance!

DW

I need to think about a mathematical algorithm to deal with this theorem- finding pseudo-primes ,aka, Carmichael numbers.

When I'm dealing with huge numbers ,it is very difficult,let's say:

a is 5, n is 200

than getting a number like 5^200 is stupid, and thus I need another method which will prevent the calculation of this number.

anybody can point me to the right direction?

another thing that I noticed is, if we do the test for non prime numbers such as 15

then we get pairs of reminders, I mean:

(7^15)%15 =13

(13^15)%15=7

just something cool(it's not just for these numbers!! )

Thanks in advance!

DW

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