Why isn't {0}^{3}+{0}^{3}={0}^{3} a proof for Fermat's Last Theorem?

[Angel11]

Hello, It is me again.So i was watching some math videos and i came across Fermat's Last Theorem which was very intersting.But i was confused because i wondered for a second and sayed "well if A,B and C are equal then they could be 0 to prove it" but at the same time i thought "well if it works something like the pythagorean theorem then that would be impossible because if a triangle has 3 sides with the length of 0 then there would be nothing" BUT again i also thought "But Fermat's Last Theorem doesn't say anything about a right triangle or any triangle it is just the formula" So my question is:Why isn't {0}^{3}+{0}^{3}={0}^{3} proof (or on any other power with n>2)

 

[MarkFL]

I've moved this thread from Differential Equations to Number Theory as that's a better fit.

From Wikipedia:

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers $a$, $b$, and $c$ satisfy the equation $a^n+b^n=c^n$ for any integer value of $n$ greater than 2. The cases $n=1$ and $n=2$ have been known to have infinitely many solutions since antiquity.

 

[Angel11]

oh i didn't realize the "positive number" how stupid of me. Also thanks for moving the thread to number theory. I put it hear because i didn't know where to put it and also thank you for replying

 

[MarkFL]

oh i didn't realize the "positive number" how stupid of me.

I don't think there's anything "stupid" about investigating theorems. It can be easy to miss details, and so asking about it is smart. :D

Also thanks for moving the thread to number theory. I put it hear because i didn't know where to put it and also thank you for replying

In the future, if you are unsure about where to post a thread, just make your best guess (as you did for this thread), and then use the post reporting feature to call the thread to the attention of the staff.

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