Friday, 4 April 2014

number theory - Computing bmods with large exponents by paper and pencil using Fermat's Little Theorem.

I'm having a bit of trouble computing mods of large numbers using Fermat's Little Theorem.




For example, how would you compute 7^{435627650}\mod 13? The solution given is




435627650\mod 12=2, so 7^2\mod{13} = 10.




In general, how does one solve this type of question with large exponents and mods by paper and pencil? I'm also a bit confused about where the 12 came from and how this problem was solved.

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