
Simple Proof of Fermats Last Theorem: Is There Any Mistake Here? - Mi_Ka_
https://github.com/TheDeepThinker/fermats-last-theorem
======
nanis
See also

[https://www.scribd.com/document/288757467/FERMAT-S-LAST-
THEO...](https://www.scribd.com/document/288757467/FERMAT-S-LAST-THEOREM-FROM-
THE-GENERALIZED-LAW-OF-COSINES)

[http://vixra.org/pdf/1506.0047v1.pdf](http://vixra.org/pdf/1506.0047v1.pdf)

[https://math.stackexchange.com/questions/1845074/why-cant-
we...](https://math.stackexchange.com/questions/1845074/why-cant-we-use-the-
law-of-cosines-to-prove-fermats-last-theorem/1850060)

[http://fermatslasttheorem.blogspot.com/2005/08/another-
false...](http://fermatslasttheorem.blogspot.com/2005/08/another-false-proof-
russian-professor.html)

~~~
Mi_Ka_
thanks a lot for sharing these links. Specially this one-
[http://fermatslasttheorem.blogspot.com/2005/08/another-
false...](http://fermatslasttheorem.blogspot.com/2005/08/another-false-proof-
russian-professor.html)

I understand, I need to prove that- cos θ is irrational for all θ, where
60<θ<90\. Which is not actually true.

------
allthatglitters
Fermat's Last Theorem is easily demonstrated using the binomial theorem -
simple algebra. It is dismissed as a proof because most fail to "see" or
"understand" variables - particularly mathematicians. Fermat gave us a hint as
to his "demonstration" by where he wrote his comment (
[https://en.wikipedia.org/wiki/Diophantus_II.VIII](https://en.wikipedia.org/wiki/Diophantus_II.VIII)
). The difference of two squares can - in some cases - be a square -
Pythagorean triples! The difference (or sum) of two integers raised to a power
greater than two - nope.

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codemaniac
How does cos(theta) produce irrational values for 60 deg <= theta <= 90 deg?

~~~
Mi_Ka_
That is what I knew. For example- cos 75 = (√2(√3 – 1))/4

For testing you can visit here-
[http://www.webconversiononline.com/trigonometry-
calculator.a...](http://www.webconversiononline.com/trigonometry-
calculator.aspx?anglein=degree&type=cosine&of=85)

~~~
nanis
cosine is a continuous function. Rationals are dense in reals etc. eg,
arccos(1/3)

~~~
Mi_Ka_
Yes, arccos(1/3) = 70.5287794 degrees

~~~
gus_massa
The important point is that

cos(arcos(1/3)) = cos(70.5287794... degrees) = 1/3

that is a rational value.

