Results 1 to 5 of 5

Math Help - Demonstration using congruency modulo m

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    3

    Demonstration using congruency modulo m

    Well, i am stuck with a problem. I have to prove that 7|(3^(2n+1) + 2^(n+2)) using the modulo m congruency.

    Well this will mean that 3^(2n+1) + 2(n+2) mod 7 = 0, but i cant find a whay to prove the initial expression.

    Any ideeas?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,545
    Thanks
    780

    Re: Demonstration using congruency modulo m

    3^{2n+1}=3\cdot9^n, and 9\equiv2\pmod{7}...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2011
    Posts
    3

    Re: Demonstration using congruency modulo m

    Thanks, i will give it a try.
    I will post a little later what i have succeded to solve. And if you will have some free time i will ask you to look at it.
    Thanks again.
    Last edited by Adrian111; December 13th 2011 at 03:04 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2011
    Posts
    3

    Re: Demonstration using congruency modulo m

    This should be : (3*9^n +2^n*4 ) eq (3*2^n + 2^n*4) eq 7*2^n mod 7 = 0 -> 7 | (3 ^(2n+1) + 2^(n+2)).

    It it is right?

    Also any iddeas for prove that 641|(2^32 + 1)?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,545
    Thanks
    780

    Re: Demonstration using congruency modulo m

    Quote Originally Posted by Adrian111 View Post
    This should be : (3*9^n +2^n*4 ) eq (3*2^n + 2^n*4) eq 7*2^n mod 7 = 0 -> 7 | (3 ^(2n+1) + 2^(n+2)).

    It it is right?
    Yes.

    Quote Originally Posted by Adrian111 View Post
    Also any iddeas for prove that 641|(2^32 + 1)?
    2^32 is not such a big number... You can also find 2^16 mod 641, then square it and take the remainder again. Or find 1024 mod 641, raise it to power 3 and multiply by 4.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modulo of squares = modulo of roots
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: December 1st 2009, 09:04 AM
  2. Help with congruency
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: October 20th 2009, 02:41 AM
  3. Congruency
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: March 7th 2009, 01:14 PM
  4. Need help with CONGRUENCY!!! @__@?
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 29th 2007, 11:59 PM
  5. Congruency
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 15th 2007, 08:35 PM

Search Tags


/mathhelpforum @mathhelpforum