Diophantine equations and class numbers of imaginary quadratic fields (Q2717944)
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scientific article; zbMATH DE number 1606094
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Diophantine equations and class numbers of imaginary quadratic fields |
scientific article; zbMATH DE number 1606094 |
Statements
19 February 2002
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Diophantine equations
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class number
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cryptography
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Diophantine equations and class numbers of imaginary quadratic fields (English)
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In order to support the realization of some quadratic field cryptosystems, the authors consider the integer solutions \(x,y\) of the Diophantine equation NEWLINE\[NEWLINE Ax^2+\mu_1B=K((Ay^2+\mu_2B)/K)^n NEWLINE\]NEWLINE where \(A,K\) are natural numbers, \(B=1,2,4\); \(\mu_i=-1,1\); \(n>1\) is odd and we assume that the \(n\)-th power of the prime divisors of \(K\) do not divide \(K\). Moreover some divisibility properties of the class numbers of certain imaginary quadratic number fields is proved.
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