The subset sum problem is finding a solution $x \in \{0,1\}^n$ such that $$\sum_{i=1}^n a_i x_i = c,$$ for $a_i, c \in \mathbb{F_q}$ (also possible for $a_i,c \in \mathbb Z$).
I know that there exists a pseudo polynomial solution to this via dynamic programming. Sadly I am not very skilled at dynamic programming yet so I was wondering if a pseudo polynomial solution was possible to the following variation on a multiple subset sum problem.
Instead of $1$ equation we are working with $2$ or more, so we need to find a solution $x \in \{0,1\}^n$ such that $$\sum_{i=1}^n a_i x_i = c_1,$$ $$\sum_{i=1}^n b_i x_i = c_2,$$ for $a_i,b_i, c_1, c_2 \in \mathbb{F_q}$.
To give you some intuition, when we would have $n$ such equations this would be solvable via Gaussian elimination.
In this case all the coefficients are positive and bounded.
I was wondering if this would be solvable via dynamic programming such that we would have a pseudo polynomial algorithm or if this isn't possible an explanation why.
I hope you guys can help me!
