wrote:

> Prove this Theorem:

Pythagorean Triplets must be of the form

>

> " If p is a ODD prime number then the following Diophantic Equation

>

> p^2+(p+k)^2=q^2

>

> has only one solution. (p, k ,q) integers.

>

> k=((p-2)*p-1)/2

>

> q=(p^2+1)/2 "

p = a^2 - b^2 = (a+b)*(a-b)

p+k = 2ab

q = a^2 + b^2

For p to be prime, a-b=1. Simple substitution finishes the proof.

William

Poohbah of oddperfect.org