# too many for loops

I am trying to solve a Diophantine system with more than 20 variables. I have been trying to use:

\

```
for a in srange(1,100):
for b in srange(1,a+1):
.
.
.
if (a+b+...)^(1\2) in ZZ and if (a+b+...)^(1/3) in ZZ:
print(a,b,...)
```

The problem is I have more than 20 variables and hence more than 20 of these for loops and Python doesnt allow that. Any help on an easy workaround would be greatly appreciated! This is not for homework or anything, I am just trying to do some computational research on Diophantine systems and I am running into some trouble.

You could construct a polyhedron based on the ranges in your

`for`

loops, and then iterate over the integral points of that polyhedron. I don't know how fast or slow this is, though.