Thread: factors

2n^2=m^2

Why is 2 a factor of m?

Put this into this form:



It is like factorising a number.

You can divide m^2 by 2 without getting a remainder, but a quotient equal to n^2.

I hope it helps.

Originally Posted by Stuck Man

2n^2=m^2

Why is 2 a factor of m?

So, m and n are integers.

If m^2 is twice n^2 that means m^2 is even. (Which is the same as saying 2 is a factor of m^2.) But if m^2 is even then m must also be even.

As it turns out, we know something stronger: that 4 is a factor of m.

Are you looking at a proof that the square root of 2 is irrational, by chance?

Yes good guess.

if m is even say 2k for some integer k, then and so is even.

if m is odd say 2k+1 for some integer k, then is odd.

so if 2 divides , then m^2 is even and by above m is even and so 2 divides m.

This has been more complicated than I first thought. Wikipedia has the full proof which was useful.