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

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Fermat's Last Theorem states that no three positive integers can satisfy the equation a^n + b^n = c^n for n greater than 2. The confusion arises from considering the case where a, b, and c are equal to zero, which does not apply since the theorem specifically requires positive integers. The discussion highlights the importance of understanding the conditions of mathematical theorems, as well as the value of asking questions to clarify concepts. Participants acknowledge the oversight regarding the requirement for positive numbers and encourage continued inquiry into mathematical topics. Engaging with such theorems is a valuable learning experience.
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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)
 
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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.
 
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
 
Angel1 said:
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

Angel1 said:
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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