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Solve the equation

Number theory
Nikos Athanasiou
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Joined: Thu Nov 19, 2015 7:27 pm

Solve the equation

(i) Let $K = \mathbb{Q} (a)$ , where $a$ is a root of $X^2 - X + 12$ in $\mathbb{R}$ . Compute the class group of K.

(ii) Show that the equation $y^2 +y + 12 =3 x^5$ does not have any integer solutions.