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I'm trying to generate the set of solutions of a specific diophantine equation over Z[i]. The equation is the following:

$$z_1^2 + z_2^2 + z_1*z_2 + 39 = 0$$

with $z_1$ (resp $z_2$) such that $\exists a,b \in Z\mathbb{Z} , z_1$ (resp $z_2$) $= a + ib$

Is there a specific tehnique to deal with Gaussian Integers in Diophantine equations ?

Regards

2 added 70 characters in body

I'm trying to generate the set of solutions of a specific diophantine equation over Z[i]. The equation is the following:

z1^2

$$z_1^2 + z2^2 z_2^2 + z1*z2 z_1*z_2 + 39 = 00$$

with zi = a+ib $z_1$ (resp $z_2$) such that $\exists a,b \in Z), z_1$ (resp $z_2$) $= a + ib$

Is there a specific tehnique to deal with Gaussian Integers in Diophantine equations ?

Regards

1

# Diophantine equation over Z[i]

I'm trying to generate the set of solutions of a specific diophantine equation over Z[i]. The equation is the following:

z1^2 + z2^2 + z1*z2 + 39 = 0

with zi = a+ib (a,b in Z)

Is there a specific tehnique to deal with Gaussian Integers in Diophantine equations ?

Regards