- #1

gottfried

- 119

- 0

## Homework Statement

If a and b divide n prove or disprove that a.b divides n.[a,b,n are positive intergers]

## Homework Equations

## The Attempt at a Solution

Suppose a.b does not divide n.

Then [itex]\frac{n}{a.b}[/itex]=I [I must not be a postitive interger]

[itex]\frac{n}{a.b}[/itex]=[itex]\frac{1}{a}[/itex].[itex]\frac{n}{b}[/itex] since a divides n it follows that n=a.x where x is a positive interger.

Therefore[itex]\frac{x}{b}[/itex]=I

This implies that the quotient of two positive intergers cannot be an interger and this is a contradiction.

I have a feeling this proof is not sufficient since it is a only a contradiction in certain cases where b divides x. If anybody could tell me if this proof is sufficient and/or give me a better one that would be appreciated.