New Solutions of $d=2x^3+y^3+z^3$
Allan J. MacLeod
TL;DR
This paper explores methods to find large integer solutions to the equation d=2x^3+y^3+z^3, successfully identifying 28 solutions for |d|<10000 using an adapted LLL-reduction technique.
Contribution
It introduces an adaptation of Elkies' LLL-reduction method for solving a specific cubic Diophantine equation, leading to new solutions.
Findings
Found 28 solutions for |d|<10000
Demonstrated effectiveness of adapted LLL method
Extended known solutions for the equation
Abstract
We discuss finding large integer solutions of by using Elsenhans and Jahnel's adaptation of Elkies' LLL-reduction method. We find 28 first solutions for .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Cryptography and Residue Arithmetic · Coding theory and cryptography