Results 1 to 2 of 2

Math Help - Fermat's Little Theorem

  1. #1
    RAz
    RAz is offline
    Junior Member RAz's Avatar
    Joined
    May 2008
    From
    Canada
    Posts
    54

    Wink Fermat's Little Theorem

    I want to use Fermat's Little Theorem to deduce that

    13^{16n+2} + 1

    is divisible by 7, where n is a positive integer.

    Does this have anything to do with modular arithmetic? D:
    If so, would I set it up like 13^{16n+2} \equiv 1 (mod 7)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,
    Quote Originally Posted by RAz View Post
    I want to use Fermat's Little Theorem to deduce that

    13^{16n+2} {\color{red}-} 1

    is divisible by 7, where n is a positive integer.

    Does this have anything to do with modular arithmetic? D:
    If so, would I set it up like 13^{16n+2} \equiv 1 (mod 7)
    You made a typo... it's a minus sign, not a + sign.

    Anyway, you don't need to use Fermat's little theorem.

    Indeed 13\equiv -1 (\bmod 7) \Rightarrow 13^2 \equiv 1(\bmod 7)

    Hence 13^{16n+2}=(13^{2(8n+1)})=(13^2)^{8n+1}\equiv 1(\bmod 7) \quad \square
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fermatís Theorem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: September 27th 2011, 07:52 PM
  2. Replies: 4
    Last Post: January 10th 2011, 09:51 AM
  3. Fermat's Last Theorem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: June 18th 2010, 02:33 AM
  4. Fermat's Little Theorem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 19th 2009, 10:47 PM
  5. Fermat's Little Theorem Help [again]
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: October 28th 2008, 09:15 AM

Search Tags


/mathhelpforum @mathhelpforum