Thread: is this a 'safe' assumption?

Hi,

If I have the following equation



and it is known that x and y are both non-equal, non-zero, even integers

then z will even and can be written

so that

It is also required that z be a square integer

so it can be rewritten

So with the above constraints I believe that



can be rewritten



so



Have I made any fundamental mistakes anywhere?

Many thanks

Pro

Given all the assumptions you made, that is correct.

Thanks HallsofIvy, glad to have someone check it over

Pro

What if y ≥ 2x ?

Originally Posted by SammyS

What if y ≥ 2x ?

Thanks SammyS.

That's true but the fact that z is a square implies

Originally Posted by procyon

and it is known that x and y are both non-equal, non-zero, even integers
then z will even and can be written
so that

x and y can also be odd ... multiplications by evens (4,8 in your case)
always give even results....

Originally Posted by procyon

Thanks SammyS.

That's true but the fact that z is a square implies

Usually the requirements are written at the beginning of the problem, so I missed the fact that z can be written as a square.

Originally Posted by Wilmer

x and y can also be odd ... multiplications by evens (4,8 in your case)
always give even results....

Thanks Wilmer.

That's true but x and y odd doesn't fit with other, simultaneous, equations I'm working with, so I thought I'd just state they're even in this case. x and y odd is valid though for a seperate set of equations.

Pro

Originally Posted by SammyS

Usually the requirements are written at the beginning of the problem, so I missed the fact that z can be written as a square.

Hi SammyS,

Yes, sorry about that. I was thinking whilst wrting instead of before

Pro

Originally Posted by procyon

That's true but x and y odd doesn't fit with other, simultaneous, equations I'm working with, so I thought
I'd just state they're even in this case. x and y odd is valid though for a seperate set of equations.

Disagree; x and y odd will work with the equations you've shown.
No separate set is required...let's see if Sammy agrees...

Originally Posted by Wilmer

Disagree; x and y odd will work with the equations you've shown.
No separate set is required...let's see if Sammy agrees...

I think if you re-read my previous reply, you'll find that I did actually agree with you on this

I'm actually saying that this equation was derived by setting other values to even

i.e.

guarantees a is a positive even integer if b is any integer > 0
guarantees a is positive odd integer if b is any integer ≥ 0

You might see the whole thing soon. At the minute I seem to have

2(odd integer) - (different [or same] odd integer) = even integer

which would prove what I'm trying to calculate is impossible.

[edit]
damn, turned out to be odd, lol
[/edit]

Pro