I need to solve the following problem.
Let $A=\{a_0,a_1,a_2,\cdots,a_k\}$
Find $a_i$ such that:
$|A|\geq 3$
$a_i\in \mathbb{N}$ and $a_i\in [32,127]$
$p=\sum_i a_i$ is prime
and $\sum_i a_i = \prod_i a_i \mod n$ for some $n\in\mathbb{N}$
I tried using the mixed integer linear programming solver in sage (Docs), but that clearly failed since the system is not linear.
I cannot seem to find any literature on this, does anyone know of any efficient solutions for problems like this? I wondered if this can be interpreted as a lattice problem like CVP(Closest vector problem) and solved that way, but I'm not sure where to start with this approach.