On searching for solutions of the Diophantine equation x3 + y3 +2z3 = n
نویسنده
چکیده
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 been found. We found three new integer solutions for n = 183, 491 and 931 in the range of |z| ≤ 5 · 107.
منابع مشابه
On Searching for Solutions of the Diophantine Equation
We propose a new search algorithm to solve the equation x3+y3 + z3 = n for a fixed value of n > 0. By parametrizing |x| =min(|x|, |y|, |z|), this algorithm obtains |y| and |z| (if they exist) by solving a quadratic equation derived from divisors of |x|3 ± n. By using several efficient number-theoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. ...
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ورودعنوان ژورنال:
- Math. Comput.
دوره 69 شماره
صفحات -
تاریخ انتشار 1997