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.
- loga X + logb Y = logc 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.
- (logc X / logc A) + (logc Y / logc B) = logc Z. Converting to the same base.
- Side notes:
- log5 9/ log5 3 + log5 16 / log5 4 = log5 25
- log5 (9/3 * 16/4) = log5 25
- logc (XY/AB) = logc Z
- (XY/AB) = Z
- (logc X / logc A) = (logc Y / logc B). Since all terms equal n.
- (logc X / logc A)/ (logc Y / logc B) = 1.
- (logc X / logc A) + (logc Y / logc B) = 2.
But we already said n > 2, thus logc Z cannot be greater than 2.
[Hahah! The errors here are super obvious!]