I need to solve a system of 36 polynomial equations of degree 2 with integer coefficients in 36 variables over integers. (I do not need rational, real or complex solutions)
I know that the system has at least one solution in integers.
I can use different methods such as eliminating variables one by one, using resultants or using Gröbner basis. None of these methods seems to be efficient for 36 variables and 36 equations.
Do you know a better method? How long should it take to solve it? Can I take as an advantage of knowing that one integer solution exist somehow?