Results 1 to 2 of 2

Math Help - show that if (a,b)=1,c>0, then (a+bx,c)=1 for some x

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    22

    show that if (a,b)=1,c>0, then (a+bx,c)=1 for some x

    Salutations! I am stuck with this interesting problem:
    Let (a,b)=1 and c>0. Prove that there is an integer x such that (a+bx,c)=1.

    Thanks for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
    Posts
    408

    Dirichlet

    This follows almost immediately from Dirichlet's Theorem on Arithmetic Progressions, which states that given any two coprime numbers a and b, there exists an infinite number of primes of the form a+bx. Since c has only a finite number of prime factors, there must be some x such that a+bx is prime and does not divide c.

    Sorry for simply referring you to another theorem. I leave it to someone else to find an elementary proof.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using the MVT to show this
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 25th 2010, 11:19 AM
  2. Show the sum
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 21st 2010, 03:28 AM
  3. Show that f o g is one-to-one
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 24th 2010, 06:29 PM
  4. Show that ln5 < 1 + 1/2 + 1/3 + 1/4.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2009, 01:29 AM
  5. how to show show this proof using MAX
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 14th 2009, 12:05 PM

Search Tags


/mathhelpforum @mathhelpforum