A New Method of Solving Diophantine Equation a3 + b3 + c3 = d
Keywords:
Diophantine equations, the sum of three cubes, Parametric solutions, Polynomial identitiesAbstract
The article is dedicated to the famous Diophantine equation of the form a 3+b 3+c 3 = d. We solve this problem in some particular cases. Using the package Mathematica 11 we find an effcient algorithm to solve this problem. This algorithm is simpler and uses a significantly smaller number of operations than the other known algorithms for solving these equations.
References
G. Payne and L. N .Vaserstein, " Sums of three cubes" , The Arithmetic of Function Fields, de Gruyter, pp. 443-454 1992.
D . H .Lehmer, " On the Diophantine equation" ,J. London Math. Soc., vol. 31 , pp. 275-280, 1956.
K. Koyama, " Tables of solutions of the D iophantine equation" , Mathematics of Computation, vol. 62, pp. 941-942, 1994.
D . Bernstein, " Three cubes" , Online. Available: http://cr.yp.to/threecubes.html.
N. D.Elkies, " Rational points near curves and small nonzero jx 3 y 2 j via lattice reduction" , Algorithmic number theory (Leiden 2000), Lecture Notes in Computer Science 1838, Springer, Berlin, pp. 33-63, 2000.
D R. Heath-Brown, " The density of zeros of forms for which weak approximation fails" , Math. Comp., vol. 5 9, pp. 613-623, 1992.
M. Beck, E. Pine, W. Tarrant and K. Yarbrough Jensen, " New integer representations as the sum of three cubes" , Math. Comp., vol. 76, pp. 1683-1690, 2007.
D . R. Heath-Brown, W. M. Lioen and H . J. J. te Riele, " On solving the Diophantine equation on a vector computer" , Math. Comp., vol. 61 , pp. 235-244, 1993.
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