In this video I go through a proof of the fact that the equation x^3+y^3=z^3 has no solutions for natural numbers x,y,z. Any equation of this form is commonly referred to as a "special case of Fermat's Last Theorem". What is Fermat's Last Theorem??: Euler's original proof: *In regards to the statements made at around 4:00, I debated whether to make a 20-30 minute video including a proof of these statements, or a 5 minute video without. I decided that the statements themselves, while not at all obvious, have little to do with the flow of the proof. Euler himself proved these statements separately, and simply referenced them. If you are interested, here is a quite badly written, long-winded proof of the statements written up by me: Also I should add I find it mind-boggling how Euler worked this out. But this would not even be considered something he is well known for. Just one of the many incredibly difficult problems he solved, that makes him truly a one of a kind genius. ❤️ ❤️ ❤️ Support the channel ❤️ ❤️ ❤️