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
∴ ca^2
> a^3 and cb^2 > b^3
=>
ca^n > a^n and cb^n > b^n
=>
Fermat’s Last Theorem. QED.