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Date registered: Aug 2002

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**(Thread Starter)**

Ok, let me help you

so we start with this equality: x^n + y^n = Z^n but we want to prove that it's not an equality, that is there are no solutions to prove said equality.

Ok, let's do this:

Suppose I do this: ((z^n)^2)^1/2 do you agree that it will give me back z^n?

if so, then let's do that to the other side of the equality:

((x^n + y^n)^2)^1/2 are you ok with that?

if so, then let's expand that a little bit:

((x^n + y^n)(x^n + y^n))^1/2 so far so good?

Let's multiply the members:

(x^2n + 2x^n.y^n + y^2n)^1/2 = z^n You're still with me?

What about I square both sides?

x^2n + 2x^n.y^n + y^2n = z^2n

Now the interesting part: suppose m = 2n

we get back:

x^m + y^m + 2x^m/2. y^m/2 = z^m

Wait a minute! do you see something? Did you just see what happened?

if x^m + y^m can be equal to z^m then we prove equality if we can prove that we can have x and y where 2x^m/2. y^m/2 = 0. Is this possible for x and y never being zero?

Do you see anything wrong with my approach? I have a feeling I made a booboo somewhere but then again, it's Sunday morning.