The proof for Fermat's Last Theorem

- Ramanraj K

12^th June, 2019

Fermat's Last Theorem states it is impossible for a cube to be written as the sum of two cubes, and more generally, no three positive integers a, b, c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. He remarked that the proof was too long to fit in the narrow margin of the book he made the note. The proof:

Pythagoras theorem states:

c^2 = a^2 + b^2

If we multiply both sides by c,

c^3 = ca^2 + cb^2

Since the hypotenuse is greater than the sides, c > a and c > b

¡à ca^2 > a^3 and cb^2 > b^3

=> ca^n > a^n and cb^n > b^n

=> Fermat¡¯s Last Theorem. QED.