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fritzh

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## Homework Statement

28. Prove the given statement:

If the product of two integers is not divisible by an integer n, then neither integer is divisible by n.

## Homework Equations

Proof by contraposition

## The Attempt at a Solution

Originally the problem states:

(xy/n)'→(x/n /\ y/n)'

This seems like a handy time for contraposition because it makes more intuitive sense that:

(x/n /\ y/n) [itex]\rightarrow[/itex] (xy/n^2)

To which I think

a=((k)(k+1))/n^2

Where it gets hazy is where to go from here. If I wanted to do proof by induction then I would need some guidance on what to aim for. Would it be:

(k+1)(k+2)/(n^2)=a

?

Any advice/guidance would be appreciated.