# Solving diophantine equations of 4-5 variables

I need to solve a certain set of diophantine equations--unfortunately they are not linear, and have 4-5 variables. What are good methods of attacking these equations? Using mathematica I am able to find examples of solutions, but not classifications of every solution. Here are some examples of the equations:

$b^2 + c (2 + c + d + e) = 2 d + b (1 + c + 3 d + e)$

$b + (1 + b + c) (1 - 2 b - c + d + 3 e + f) = e + (1 + d + e) (1 + e + f)$

$1/2 e (1 + e) + (1 + b + c) (1 - b - c + d + 2 e + f) = 1/2 b (1 + b) + (1 + d + e) (1 + e + f)$

In total, there are 8 equations similar to this I need to solve. So I'm looking for general methods as well as potential solutions

• The wording is not clear. Just write what the equation should be solved. – individ Sep 18 '17 at 11:03
• It is very difficult to solve such systems. If possible it is to simplify the system. For example finding the interdependent parameters. 3 the equation is actually an algebraic - in fact with 4 degree. A lot of effort must be applied in order to solve it. There is a method for solving systems of nonlinear equations. Some of the formulas collected there. artofproblemsolving.com/community/… But this method cannot be used. – individ Sep 20 '17 at 4:46