I’m wanted to play around with Fermat’s Last Theorem, and the proof seemed very obvious to me! Find the errors!

A^{n} + B^{n} ≠ C^{n} if A, B, C are whole numbers and *n* > 2.

Let’s try for a reductio ad absurdum. Let’s put Fermat’s claim in logarithmic form.

- log
_{a}X + log_{b}Y = log_{c}Z in which all terms equal*n, n > 2.* - If a, b, and c are whole numbers all raised to the same power
*n*then we can rewrite the above. - (log
_{c}X / log_{c }A) + (log_{c}Y / log_{c }B) = log_{c}Z.*Converting to the same base.***Side notes:**

- log
_{5}9/ log_{5}3 + log_{5}16 / log_{5 }4 = log_{5}25 - log
_{5}(9/3 * 16/4) = log_{5}25 - log
_{c}(XY/AB) = log_{c}Z

- (XY/AB) = Z

- (log
_{c}X / log_{c }A) = (log_{c}Y / log_{c }B).*Since all terms equal n.* - (log
_{c}X / log_{c }A)/ (log_{c}Y / log_{c }B) = 1. - (log
_{c}X / log_{c }A) + (log_{c}Y / log_{c }B) = 2.

But we already said n > 2, thus log_{c} Z cannot be greater than 2.

[Hahah! The errors here are super obvious!]