• Corpus ID: 218718978

Sum of Three Cubes via Optimisation.

@article{Lazov2020SumOT,
  title={Sum of Three Cubes via Optimisation.},
  author={Boian V. Lazov and T. Vetsov},
  journal={arXiv: Number Theory},
  year={2020}
}
By first solving the equation $x^3+y^3+z^3=k$ with fixed $k$ for $z$ and then considering the distance to the nearest integer function of the result, we turn the sum of three cubes problem into an optimisation one. We then apply three stochastic optimisation algorithms to this function in the case with $k=2$, where there are many known solutions. The goal is to test the effectiveness of the method in searching for integer solutions. The algorithms are a modification of particle swarm… 
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