# On searching for solutions of the Diophantine equation x3 + y3 +2z3 = n

```@article{Koyama2000OnSF,
title={On searching for solutions of the Diophantine equation x3 + y3 +2z3 = n},
author={Kenji Koyama},
journal={Math. Comput.},
year={2000},
volume={69},
pages={1735-1742}
}```
• K. Koyama
• Published 2000
• Mathematics
• Math. Comput.
We propose an efficient search algorithm to solve the equation x3 + y3 + 2z3 = n for a fixed value of n > 0. By parametrizing |z|, this algorithm obtains |x| and |y| (if they exist) by solving a quadratic equation derived from divisors of 2|z|3±n. Thanks to the use of several efficient numbertheoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. We performed a computer search for six values of n below 1000 for which no solution had previously…
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