In this paper estimates of linear forms in elliptic logarithms are applied to solve the problem of determining, for given n greater than or equal to 2, all sets of n consecutive cubes adding up to a perfect square. Use is made of a lower bound of linear forms in elliptic logarithms recently obtained by Sinnou David. Complete sets of solutions are provided for all n between 2 and 50, and for n = 98.
机构:
Fermilab Natl Accelerator Lab, Particle Theory Dept, Batavia, IL 60510 USAFermilab Natl Accelerator Lab, Particle Theory Dept, Batavia, IL 60510 USA
Dobrescu, Bogdan A.
Fox, Patrick J.
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机构:
Fermilab Natl Accelerator Lab, Particle Theory Dept, Batavia, IL 60510 USAFermilab Natl Accelerator Lab, Particle Theory Dept, Batavia, IL 60510 USA