I am a fan of Fermat, not only because my university Alma Mater was in his hometown Toulouse (France) named after him “**Lycée Pierre de Fermat (Classe Préparatoire Aux Grandes Ecoles**) ” , but also the “**Fermat’s Last Theorem” (FLT)** has fascinated for 350 years all great Mathematicians including Euler, Gauss,… until 1993 finally proved by the Cambridge Professor Andrew Wiles. Another “**Fermat’s Little Theorem**” is applied in computer Cryptography .

Below is the **explanation of (n = 4) case proved by Fermat and the latest proof by contradiction**.

**Euler Conjecture**: extends FLT to **4** or more integers if FLT still holds? (a contradiction found).

Simpsons “Fool” Equality: Proof by contradiction (odd = even)

Proof of FLT by Andrew Wiles (1993):

The proof by Contradiction of FLT (n=4) is in Part 2 of the video after 20:30 mins **(Warning**: a bit heavy)

Proof of Fermat’s Last Theorem

a^n+b^n=c^n

odd+even=odd

a^3+b^3=c^3

let c=2x+1

8x^3+12x^2+6x+1=c^3

let b=2x

b^3+12x^2+6x+1=c^3

a^3=12x^2+6x+1

Only valid solution to a is when x=0 for all

c=2x+1,2x+3,2x+5,…

n=3,4,5,…

No whole number solution for a,b,c when n>2

LikeLike