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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: No Putnam spoilers please
Replies: 15   Last Post: Dec 14, 2012 6:05 AM

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Butch Malahide

Posts: 885
Registered: 6/29/05
Re: No Putnam spoilers please
Posted: Dec 5, 2012 12:24 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Dec 4, 9:48 pm, William Elliot <ma...@panix.com> wrote:
>
> phi(13) = 12;
> 5^2012 = 5^(12 * 168 + 6) = 5^6 = 25^3 = (-1)^3 = -1 = 12 (mod 13)

Actually, 5^2012 = 1 (mod 13).

5^2 = -1 (mod 13)
5^4 = (-1)^2 = 1 (mod 13)
5^2012 = 5^(4*503) = (5^4)^503 = 1^503 = 1 (mod 13)

Your error was in your first step: 2012 = 12*167 + 8.

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