The problem of solving quadratic equations is as follows:
Suppose you are given a set of quadratic equations and are asked to find $0$-$1$ values for the variables such that all equations are satisfied. For example, consider the system $$x_1x_2-x_3 = 0$$ $$x_1x_3-x_1x_4+x_3x_4 = 1$$ $$x_1x_4-x_2x_3+x_1x_3 = 0$$ You may easily verify that the setting $$x_1=x_2=x_3=1$$ and $$x_4=0$$ satisfies all requirements.
I need to show that if we suppose that this problem is in P then the problem of integer factorization is also in P. I have no idea how to start. Please help me.
I know that the problem is in NP, because there is a polynomial verifier to it. I got stuck when I tried to find a polynomial reduction from the quadratic equation problem to integer factorization. I don't figure out how to "connect" from quadratic equations to integer factorization. I have tried to simplify the problem and construct a polynomial reduction from this problem to the problem of finding only one divisor of $n$, and if I do so, I could simply run this algorithm polynomial number of times to find the other divisors of $n$. So far I have failed at this.