Use fermats little theorem to find the remainder when 7^100,000 is divided by 11

You want to find the unique integer r satisfying 0 <= r < 11 and 7^100000 = r mod 11.

Fermat's little theorem tells you that 7^10 = 1 mod 11. Since 100000 = 10*10000, it follows that

7^100000 = 7^(10*10000) = (7^10)^10000 = 1^10000 = 1 mod 11,

so the remainder on dividing 7^10000 by 11 is 1.

For relatively prime numbers "a" and "p", Fermat's little theorem says
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