Show that:
or
Take ; and
It should be
Now, the proof I've found is nasty
We have
Let's define
M divides any linear combination ( with integer coeficients) of those 2.
So M divides: i.e.
Again: Thus:
And this goes on:
We keep on eliminating terms, the idea is to have only 1 term in the end.
If is even we eventually get: ( or the symmetric)
Whereas if n is odd:
But, since M divides a-b and (a,b)=1 then and thus we must have