I Think The Szpiro conjecture is valid

[MathDoggy]

Introduction: The Szpiro conjecture is a mathematical supposition which states that for any elliptic curve E defined over Q with discriminant |∆| always satisfies the following:


Let C(ε) be a positive integer constant
Let f be the conductor of the elliptic curve E
Let epsilon be a constant contained in N (where N is the set of natural numbers)

Condition that is conjectured to be satisfied always:

|∆| ≤ C(ε)*f raised to the 6+ε

Proof by induction:

Let P(n) be the statement of the Szpiro conjecture

Now we will prove the the validness of the case P(1), which is equal to this:
All constants are equal to 1.

|1| ≤ C(1)*1 raised to the seven

So P(1) is valid

Continously we assume that P(n) is valid therefore P(n+1) has to be proven


Demonstration of P(n+1) :

|∆| ≤ C(ε)*f raised to the 6+ε

Assume that the other part of this inequality after the discriminant does not grow, but this absurd since the product of positive integers always grows therefore the right side of the inequality is always bigger becuase the discriminant does not grow.

Q.E.D
With this proof of P(n+1) we have proved the Szpiro conjecture and the abc conjecture, Fermat´s Last Theorem, and a great set of other conjectures.

[CRGreathouse]

How does this proof change if you replace 6 with other numbers?

[MathDoggy]

Originally Posted by CRGreathouse

How does this proof change if you replace 6 with other numbers?

It does not change if the number is a positive integer

[CRGreathouse]

Originally Posted by MathDoggy

It does not change if the number is a positive integer

Where do you use the condition that the exponent is an integer?