Integral solutions in arithmetic progression for elliptic curves.
AdvisorYelez, William Y.
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PublisherThe University of Arizona.
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AbstractIntegral solutions to y² = X³ + k, where either the x's or the y's, or both, are in arithmetic progression are studied. When both the x's and the y's are in arithmetic progression, then this situation is completely solved. One set of solutions where the y's formed an arithmetic progression of length 4 have already been constructed. In this dissertation, we construct infinitely many set of solutions where there are 4 x's in arithmetic progression and we also disprove Mohanty's Conjecture by constructing infinitely many set of solutions where there are 4, 5 and 6 y's in arithmetic progression.