Question

Prove or Disprove Let a, b be integers. If a/b^2, then a/b

Answer 1

Not sure what you're asking. Are you asking "if a divides b^2, then a divides b"?

Or are you suggesting the fraction
\[ \frac{a}{b^2} \text{or } (\frac{a}{b})^2\]

In which case "If a/b^2" isn't really a statement

Answer 2

lol thats what it is on a divides b^2 it thats true then a divides b. I have to prove this statement

Answer 3

Ok that's what I thought. I'm sorry, I messed up the order initially. Can you think of a counterexample?
What if a = 9 and b=6?

Does 9|36? Yes. Does 9|6? No.

Sorry, I was confusing myself while writing this, let me know if you have any additional questions.

Answer 4

Thanks, yea I got another questions
Let a,b,c be integers. If c > 0, then gcd(ac,bc) = cgcd(a,b). Suggestion: Let d= gcd(a,b). Show cd = gcd(ac,bc)

Answer 5

If you think about this one intuitively, it should make sense. To give you a rough idea:

\[ d = \text{gcd}(a, b) \]
\[ \Rightarrow \exists m,n \in \mathbb{Z} \text{ such that } dm=a, \ dn = b \]
Multiply both sides of each equality by c
\[ c(dm)=ac, \ c(dn) = bc \]
\[ m(cd) = ac, \ n(cd) = bc \]
\[ \Rightarrow cd = \text{gcd} (ac,bc)\]

Answer 6

Thanks