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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 |
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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: 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 |
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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
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