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Compute 10^785 mod 23

Name: Anonymous 2009-10-18 21:34

I don't want the solution right away but could someone please point me in the right direction? I know there must be some trick to somehow 'cancel' the huge exponent but I don't know how to play with it.

Name: Anonymous 2009-10-22 11:07

Damn, I messed up the tags again. Final version (I hope!):

10785 = 10(23·34)+3 = 1023·34 · 103 = (1023)34 · 103

As 23 is prime, x23 mod 23 is 1 for all non-zero x. So:

(1023)34 · 103 = 134 · 103 = 103 mod 23 = 1000 mod 23 = 8

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