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## Homework Statement

http://math.stanford.edu/~vakil/putnam07/07putnam2.pdf

I am working on number 2.

So I want to find 2^70 + 3^70 mod 13.

I can use Fermat's Little Theorem to reduce the exponent to 10, but I do not know what to do next...

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- Thread starter ehrenfest
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http://math.stanford.edu/~vakil/putnam07/07putnam2.pdf

I am working on number 2.

So I want to find 2^70 + 3^70 mod 13.

I can use Fermat's Little Theorem to reduce the exponent to 10, but I do not know what to do next...

- #2

morphism

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2^2 = 4 and 3^2 = 9

and 4^5 + 9^5 = (4+9)*something.

and 4^5 + 9^5 = (4+9)*something.

- #3

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Is that true? Where does that come from?4^5 + 9^5 = (4+9)*something.

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morphism

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I see. Thanks.

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