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Homework Help: Division proof and prime

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data

    (2) P is a prime number and a and b are positive integers .
    We Know...
    p | a^6 \
    p | a^3 + b^7.
    how do i find out how to prove that p | b?

    2. Relevant equations
    if a | b, then a | bx for every x in Z
    if a | b, and a | c, then a | bx + cy for any x,y in Z.

    3. The attempt at a solution
    p | (a^3)(a^3)

    p | a^6(n) + (a^3 + b^7)m for any m,n in Z.

    I cant figure anything out about b :(
  2. jcsd
  3. Nov 2, 2011 #2


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    Science Advisor
    Homework Helper

    Do you know about prime factorization? If p|a^6 then p|a, doesn't it?
  4. Nov 3, 2011 #3
    we dont know enough about a to be able to say that?
  5. Nov 3, 2011 #4


    User Avatar
    Science Advisor

    If p is prime, then yes you do.
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