Use Fermat’s Last Theorem to prove irrational of cubic root of 2.

# Tag Archives: Fermat Last Theorem

# Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced

… (Read on) from source :

** Summary**:

Andrew Wiles’ Proof of Fermat’s Last Theorem (FLT) by contradiction :

A. Assume FLT is true for all **prime** p (Why? sufficient to prove only for prime) such that:

B. then a, b, c could be rearranged into an **Elliptic Curve**,

C. then leverage such Elliptic Curve into a **Galois Represebtation**.

D. then a **Modular Form**.

E. then leads to an **impossible** weight 2 level 2 **Modular Form**.

Hence,

**¬E -> ¬D -> ¬C -> ¬B -> ¬A (proved)**

1950s Taniyama-Shimura-Weil proved the link below:

**B -> **(via** **assume** **C) -> **D**

Andrew Wiles’ took 7 years to complete the whole proof in 1994 by proving the missing link **C -> D.**

# Proof Irrational cuberoot (2)

Assume

is rational, then

with p, q integers

After arrangement, we get

… [*]

According to Fermat’s Last Theorem, the equation [*] has no solution.

Hence, par absurd,

is **IRrational**.

# Euler’s and Fermat’s last theorems, the Simpsons and CDC6600

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)

# Quora : How likely is it that a mathematics student can’t solve IMO problems?

How likely is it that a mathematics student can’t solve IMO problems?

Is there a fear of embarrassment in being a math Ph.D. who can’t solve problems that high-school students can? by Cornelius Goh