Quote:
Originally Posted by tetramur
Minimize x1*x2 with these conditions:
x1*x2 >= N
2 <= x1 <= N1
2 <= x2 <= N1
x1 <= x2

Okay, let's try this. Suppose I want to factorize N = 91. I'll plug your conditions into my magic optimization machine, and out come the factors:
x1 = √91, x2 = √91
Wait, you wanted the solutions to be integers? Well, you're out of luck  my machine doesn't know how to solve that type of
problem in polynomial time.