Results 1 to 3 of 3

Math Help - Number theory (primes)

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    5

    Number theory (primes)

    *Evaluate (ab, p^4) and (a+b,p^4) given that (a,p^2)=p and (b, p^3)=p^2 where p is a prime


    .................note: i just use ^...it's actually p above 4...i can't draw....thanks..i mean p to the power of 4
    Last edited by blazingmath; September 6th 2009 at 03:50 AM. Reason: Deleted the drama and soap.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by blazingmath View Post
    *Evaluate (ab, p^4) and (a+b,p^4)
    given that (a,p^2)=p
    and (b, p^3)=p^2 where p is a prime
    ...
    If GCD(a, p^2) = p then a = p or a = mp (a multiple of p, m<p )

    If GCD(b, p^3) = p^2 then b = p^2 or b = k p^2 (a multiple of p^2, and  k \neq p )

    ab = mp \cdot kp^2 = kmp^3
    Thus,
    GCD( kmp^3,p^4) \, = \, p^3


    a+b = mp + kp^2 \, = \, p(m+kp)
    &
    GCD ( p(m+kp), p^4) \, = \, p

    .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    5

    primes

    thank u very much for ur reply...really thanks..god bless you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Number theory(Primes)
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: September 9th 2009, 04:54 PM
  2. Number theory (Primes)
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 9th 2009, 12:23 AM
  3. Number theory (Primes)
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: September 8th 2009, 06:15 PM
  4. Number Theory - Primes and Eulers equation
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: August 9th 2007, 12:39 PM
  5. Find All Primes of a Number
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 18th 2007, 08:19 PM

Search Tags


/mathhelpforum @mathhelpforum