Representation of integers by quadratic forms using the cornacchia algorithm
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Abstract
Cornachia's algorithm can be adapted to the case of the equation and even to the case of . For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation ). Starting from a quadratic form with two variables and an integer. We have shown that a primitive positive solution of the equation is admissible if it is obtained in the following way : we take α modulo n such that is the first of the remainders of Euclid's algorithm associated with n and α that is less than ) (possibly itself) and the equation has an integer solution in . At the end of our work, it also appears that the Cornacchia algorithm is good for the form if all the primitive positive integer solutions of the equation are admissible, i.e. computable by the algorithmic process.
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References
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