Geodesic
Exponent of class group of certain imaginary quadratic fields
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1167-1178
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Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\mathbb {Q} \bigl (\sqrt {x^2-2y^n} \bigr )$ whose ideal class group has an element of order $n$. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\mathbb {Q} \bigl (\sqrt {x^2-2y^n} \bigr )$ whose ideal class group has an element of order $n$. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
DOI : 10.21136/CMJ.2020.0289-19
Classification : 11R11, 11R29
Keywords: quadratic field; discriminant; class group; Wada's conjecture 
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Chakraborty, Kalyan; Hoque, Azizul. Exponent of class group of certain imaginary quadratic fields. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1167-1178. doi: 10.21136/CMJ.2020.0289-19

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