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

  title={On searching for solutions of the Diophantine equation x3 + y3 +2z3 = n},
  author={Kenji Koyama},
  journal={Math. Comput.},
  • 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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