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STUDIA MATHEMATICA - Issue no. 3 / 2019 | |||||||
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AN ELLIPTIC DIOPHANTINE EQUATION FROM THE STUDY OF PARTITIONS. Authors: DORIN ANDRICA, GEORGE C. ŢURCAŞ. |
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Abstract: We present the elliptic equation X3 +2 = Y 2 as the first in a sequence of Diophantine equations arising from some new results in the theory of partitions of multisets with equal sums. Two proofs for Theorem 2.3, showing that the only integer solutions to this equation are (-1, 1) and (-1,-1), are given. Mathematics Subject Classisifiation (2010): 14G05, 11P57, 11Y50. Keywords: Elliptic curves, partitions of a set, Mordell equations, Lutz-Nagell theorem.
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