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April 27th, 2019, 09:15 AM   #11
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I finally got the photo posted.

If you accept the equation Z^n = X^n +Y^n, then X^2 + Y^2 < Z^2.

While we don't know how much X^2 + Y^2 is less than Z^2, we can assign a variable, e/f, to represent this unknown.

So, X^2 + Y^2 = e/f * Z^2. The range of e/f is between 1 and 2^1/2.

All your questions refer to using a ratio e/f = 1, which is true for the case when n = 2. i.e. X^2 + y^2 = z^2 (WHEN TALKING ABOUT TRIPLETS), in this case we are talking about how much smaller X^2 + Y^2 are to Z^2 when Z^n = X^n + Y^n.

IMG_6049 (1).jpg

Last edited by skipjack; April 27th, 2019 at 03:41 PM.
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April 27th, 2019, 11:56 AM   #12
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Quote:
Originally Posted by michaelcweir View Post
If you accept the equation Z^n = X^n +Y^n,
WEIRd looking equation

Last edited by skipjack; April 27th, 2019 at 03:40 PM.
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April 27th, 2019, 03:46 PM   #13
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Originally Posted by michaelcweir View Post
I finally got the photo posted.
I don't see what relevance it has to FLT.

Your first couple of posts at least stated complete arguments. Lately nothing you write makes sense at all.

I don't follow your calculation in the diagram. And one of the denominators is unclear, is it n^2? Or x^2 or z^2?
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April 27th, 2019, 04:04 PM   #14
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That denominator appears to be x². I've no idea why x and y sometimes appear instead of X and Y for no apparent reason.
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April 27th, 2019, 05:01 PM   #15
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I think if you inspect the diagram photo I just uploaded, you will understand where where the Xaand Y's come from.
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April 27th, 2019, 05:10 PM   #16
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Originally Posted by michaelcweir View Post
I think if you inspect the diagram photo I just uploaded, you will understand where where the Xaand Y's come from.
Ok you proved that $z^{n - 2} < x^{n-4} + y^{n-4}$. You didn't prove that $x^2 + y^2 < z^2$. How does this relate to FLT?

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Originally Posted by michaelcweir View Post
If you accept the equation Z^n = X^n +Y^n, then X^2 + Y^2 < Z^2.
I don't think this is true. Take $2^5 + 3^5 = z^5$. Then $z = 275^{\frac{1}{5}} \approx 3$.

But $2^2 + 3^2 = 13$ and $3^2 = 9$. And nothing you wrote uses the fact that $x$, $y$, and $z$ are integers. So here's a counterexample to your claim.
Thanks from topsquark

Last edited by Maschke; April 27th, 2019 at 05:56 PM.
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April 28th, 2019, 03:21 PM   #17
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Quote:
Originally Posted by Maschke View Post
Ok you proved that $z^{n - 2} < x^{n-4} + y^{n-4}$. You didn't prove that $x^2 + y^2 < z^2$. How does this relate to FLT?

o, x2+y2<z2 and therefore x^2+y^2<z^2 has been proved by examination of number line

Suppose z^5 + X^5 + Y^5

divide both sides by Z^3

gives Z^2= X^5/Z^3 + Y^5/Z^3

Which is bigger? X^5/Z^3 or X^5/X^3?

X^5/X^3 is because the divisor , X^3, is smaller than Z^3
Similarity, Y^3 is smaller than Z^3

So, I just proved z^2< x^2+y^2

So now if you go and assign a variable factor to the equation to get rid of the inequality, you get
x^2+y^2=e/f *z^2 where e/f is between 1 and 2^1/2

If now you go through the calculations, you come up with the answer that Y is a number less than !, in a range between 0.45 and 0.5.

Because Y is less than 1, the equation Z^n = X^n +Y^n is wrong for every choice of integers X,Y,Z. This proves FLT.



I don't think this is true. Take $2^5 + 3^5 = z^5$. Then $z = 275^{\frac{1}{5}} \approx 3$.

But $2^2 + 3^2 = 13$ and $3^2 = 9$. And nothing you wrote uses the fact that $x$, $y$, and $z$ are integers. So here's a counterexample to your claim.
The counter-example only shows that my notation for less than was the wrong one. You are correct that Z^2 < X^2 + Y^2. Fortunately, I assigned the right variable range and so the calculation was correct. The diagram also shows the right relationship between Z^2 and X^2 + Y^2. So thank you for catching the error. You did demonstrate the right inequality. So if you assign a variable, e/f, you can make the calculation and show that Y can never be an integer.

Last edited by skipjack; April 28th, 2019 at 05:42 PM.
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May 6th, 2019, 05:00 PM   #18
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Here is 3 pages showing how Y id determined to be between 0.48 and 1.
Attached Images
File Type: jpg IMG_6061.jpg (84.4 KB, 6 views)
File Type: jpg IMG_6062.jpg (82.3 KB, 2 views)
File Type: jpg IMG_6063.jpg (85.5 KB, 3 views)
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May 6th, 2019, 05:06 PM   #19
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here is page 1 of 3
Attached Images
File Type: jpg IMG_6061.jpg (84.4 KB, 1 views)
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May 6th, 2019, 05:27 PM   #20
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working out value for Y in terms of h,c/d and e/f

here are 3 pages of handwritten analysis
Attached Files
File Type: pdf fermat one20190506_18185751.pdf (9.4 KB, 0 views)
File Type: pdf fermat two20190506_18224429.pdf (8.5 KB, 0 views)
File Type: pdf fermat three20190506_18243424.pdf (7.7 KB, 0 views)
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