Description of interesting failed factor algorithm
- To factor the arbitrary positive integer z,
I found integers
h1, h2, h3,h4 such that
h1 + h2 + h3 + h4 = z
h1 * h4 - h2 * h3 = 0.
Then I expected that x = gcd(h1,h2) + gcd(h3,h4) would divided z.
Indeed, x does divide z.
x seems to always be equal to 1.
I haven't yet found a way to generate a set h1,h2,h3,h4
such that all of them are positive,
h1 + h2 + h3 + h4 = z,
h1 h4 - h2 h3 = 0.