Hi again,
Have struggled with this for a while but getting nowhere.
I've reduced this to
but can't seem to break it down any further in a similar method to my previous thread
http://www.mathhelpforum.com/math-he...tml#post674932
Any ideas would be greatly appreciated
Thanks for the reply Captain. I probably should have added that for clarity but thought since I showed
would be enough.
It's a way of finding integer roots of this (not all, but not by trial & error either) I'm trying to get, similar to the last post I mentioned
http://www.mathhelpforum.com/math-he...tml#post674932
Pro
There are no integer solutions when is odd, to see this (and how to find the other solutions) write:
Then for any factorisation of we may set
If is odd then from the second of these equations and are of different parities, but from the first they are of the same parity. This is a contradiction so for there to a solution must be even, which is not possible if (and also ) is odd.
CB
Many thanks for the above CB. I had been working at it a more difficult way as usual, lol.
I'm not sure if I have made myself clear on what it is I actually seek.
I want to be able to reduce
into some form of
even if it is like this
I'll start here
I have used the fact that z must be even and that w and x must both be even or both be odd to no avail
i.e.
is even and so there is some integer such that
let w and x both be even, so similarly, and
so we now have
which is back to the start
let's forget that z must be even but still have w and z such
It's different, but still not what I'm after.
Surely, you mean:
---------- (1)
---------- (2)
------------------------------------------------------------------------------------------
Let and
Solving (1) and (2), we get
and
So, (-1, 5, 2) is a solution.
Note that (1, 5, 2) is also a solution. (This is obtained by setting and .)
We can choose any , any even and generate a solution. Thus, there are infinitely many solutions.
Thank you so much to alexmahone and CaptainBlack for helping me with this.
Here's the whole thing in case it's of use to someone else.
(I've used p and q for the factors only because I find it easier to follow)
so
let and be factors of so that and
now
let ..........(1)
and ..........(2)
and now for the checking...
Thanks again guys
Pro