# Finding an irreducible polynomial in Z [x] but reducible in F2 [x]

Hi everyone, I've been trying to find an irreducible polynomial in Z [x] but reducible in F2 [x].

I tried using this code:

```
i = 1
a = 0
while a == 0:
R = GF(2) ['x']
for p in R(x)polynomial(i)
i = i + 1
if not p.is_irreducible():
R.change_ring(ZZ)
if p.is_irreducible():
print p
a = 1
```

As I couldn't think of a way of finding an irreducible in Z and after that changing it to F2 I decided to do it backwards.

I'm in your graceful hands and sorry for my broken English.

Homework ?

I am not going to lie to you. Yeah it is.

Hint : you are looking for a polynomial that you can factor in $\mathbb{F}_2$ but not in $\mathbb{Z}$. This might give you ideas :

Thank you, it helped a lot.