4272Re: [PrimeNumbers] Pythagoras and factoring
- Dec 3, 2001Hi, David & All!
You method (IMHO) based upon the following:
Let A be the number to factor. Using common solution to Pythagoras, we can
so that A^2+B^2=C^2.
Then B+C=(U+V)^2, B-C=(U-V)^2 as in your examples. But it is *not* common
For instance, the least solution to A^2+B^2=C^2 with A=123 is
Both your C-program and my pascal one find this solution. But,alas
205-164=41 is *not* square, neither is
All this nightmare is due to fact that common solution to Pythagoras is
and, for instance, B+C=K*(U+V)^2. Only GCD can help, or another solution to