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Searching for simultaneous arithmetic progressions on elliptic curves

Irene Garcia-Selfa·Jose M. Tornero
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Abstract

We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.

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Irene Garcia-Selfa, Jose M. Tornero. 2007-03-21. Searching for simultaneous arithmetic progressions on elliptic curves. https://arxiv.org/abs/math/0703624

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