"As we all know a solution for x² = y² + z² is 5² = 4² + 3². There are infinite solutions. But, are there any solutions for equations in the form x^n = y^n + z^n for all natural numbers n > 2? "
Good thing I just read the TG comic: Math help, so I'm fully qualified to answer this question. Whoever asked this certainly was a tricky one thinking that one cannot be smart and sexy at the same time. I know by now everyone is wondering what the answer is! After running some calculations on the blackboard...
The answer is No.
Look up "Fermat's Last Theorem" if you are a sexy math geek.
Ask me anything you want. I'll answer anything! The is the limit.