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selfAdjoint
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Why don't you start by showing why y[3x^2 +3xy + y^2] can't be a cube, and then we'll go on from there.
Originally posted by selfAdjoint
Why don't you start by showing why y[3x^2 +3xy + y^2] can't be a cube, and then we'll go on from there.
Originally posted by Russell E. Rierson
[x+y]^2 - x^2 = 2xy + y^2
3^2 = 2*4*1 + 1^2
5^2 = 2*12*1 + 1^2
7^2 = 2*24*1 + 1^2
[x+y]^3 - x^3 = 3yx^2 + 3xy^2 + y^3
y[3x^2 +3xy + y^2]
cannot be a cube.
y[2x+y] is a square.
y[3x^2 +3xy + y^2] is not a cube
y[4x^3 + 6yx^2 + 4xy^2 + y^3] is not a 4th power
Originally posted by matt grime
And that is never a cube for what reason? And the other infinite set of cases for n=3 are also false because?
I don't remember a proof that 1 more than 6 times the sum of the first N numbers is a cube, so fill in the blanks for me.
Originally posted by matt grime
The universal set? Representable? Do you practise at this or does it come naturally?
digiflux said:Princeton has gotten tremendous publicity from Wiles and his bogus "proof". That means $ pour in. They ARE protecting their crybaby, Wiles.
Fermat's Last Theorem is a famous mathematical conjecture proposed by Pierre de Fermat in the 17th century. It states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than 2.
Fermat's Last Theorem is important because it has been one of the most famous and elusive problems in mathematics for over 350 years. Many mathematicians have attempted to prove or disprove the theorem, and it has led to significant advancements in number theory and algebraic geometry.
Without knowing the specific details of your father's proof, it is impossible to determine its validity. However, it is important to note that Fermat's Last Theorem has been rigorously proven by Andrew Wiles in 1995, using advanced mathematical techniques that were not available during Fermat's time.
If you are not an expert in mathematics, it is best to consult with a mathematician or submit the proof to a reputable mathematical journal for peer review. It is also important to note that even if a proof appears valid, it may still contain errors that can only be discovered through rigorous scrutiny.
One common misconception is that Fermat himself had a proof for the theorem, which he famously claimed in the margin of his copy of Arithmetica. However, there is no evidence to support this claim, and it is more likely that Fermat was mistaken or simply teasing other mathematicians. Another misconception is that the theorem only applies to positive integers, when in fact it can be extended to include other types of numbers such as rational and complex numbers.