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

Aⁿ + Bⁿ ≠ Cⁿ 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.

1. log_a X + log_b Y = log_c Z in which all terms equal n, n > 2.
2. If a, b, and c are whole numbers all raised to the same power n then we can rewrite the above.
3. (log_c X / log_c A) + (log_c Y / log_c B) = log_c Z. Converting to the same base.
   1. Side notes:
   1. log₅ 9/ log₅ 3 + log₅ 16 / log₅ 4 = log₅ 25
   2. log₅ (9/3 * 16/4) = log₅ 25
   3. log_c (XY/AB) = log_c Z
   1. (XY/AB) = Z
4. (log_c X / log_c A) = (log_c Y / log_c B). Since all terms equal n.
5. (log_c X / log_c A)/ (log_c Y / log_c B) = 1.
6. (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!]