Proving the Division Property of Prime Numbers in Positive Integers

[PennState666]

Homework Statement

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

Homework 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.

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 can't figure anything out about b :(

 

[Dick]

Do you know about prime factorization? If p|a^6 then p|a, doesn't it?

 

[PennState666]

we don't know enough about a to be able to say that?

 

[Ibix]

If p is prime, then yes you do.