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arXiv · 2507.08337

Counting sums of two powers

Anand Patel
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Abstract

We generalize two well-known enumerative facts. The first, due to Clebsch, says that a general binary sextic form is expressible as the sum of a cube and a square in 40 different ways. The second, due to Zariski and later Vakil, states that a general pencil of binary 12-ics contains exactly 3762 cubes plus squares, ignoring scaling.

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Anand Patel. 2025-07-11. Counting sums of two powers. https://arxiv.org/abs/2507.08337

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