Logic, proof by induction

[Halo]

Hello

 

How do you show that there are no whole numbers [math]n[/math], [math]m[/math], [math]n\times m\neq 0[/math] such that [math]m\sqrt{2}+n\sqrt{2}[/math] is a rational number.

 

Thanks!

[ydoaPs]

Hello

 

How do you show that there are no whole numbers [math]n[/math], [math]m[/math], [math]n\times m\neq 0[/math] such that [math]m\sqrt{2}+n\sqrt{2}[/math] is a rational number.

 

Thanks!

 

 

You presumably (from the thread title) want to use mathematical induction. You need to have a conditional proof assuming that it is the case for any positive integers, and prove with that that it is the case for 1+any positive integer. All you need after that is the base case which is setting your integers equal to 1.