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Division proof and prime

  • #1

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 cant figure anything out about b :(
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
Do you know about prime factorization? If p|a^6 then p|a, doesn't it?
 
  • #3
we dont know enough about a to be able to say that?
 
  • #4
Ibix
Science Advisor
Insights Author
5,955
4,520
If p is prime, then yes you do.
 

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