@inbook{f4fc1ea2e74f47f0adf5f2c3451e4cbb,
title = "Equal sums of two cubes of quadratic forms",
abstract = "We give a complete description of all solutions to the equation f31+f32=f33+f34 for quadratic forms fj ∈ ℂ [x, y] and show how Ramanujan{\textquoteright}s example can be extended to three equal sums of pairs of cubes. We also give a complete census in counting the number of ways a sextic p ∈ ℂ [x, y] can be written as a sum of two cubes. The extreme example is p(x, y) = xy(x4 − y4), which has six such representations.",
keywords = "Cubic forms, diophantine equations, sextic forms",
author = "Bruce Reznick",
year = "2024",
month = sep,
doi = "10.1142/9789811277375_0035",
language = "English (US)",
isbn = "9789811277368",
series = "Monographs in Number Theory",
publisher = "World Scientific",
pages = "583--608",
editor = "Andrews, {George E} and Michael Filaseta and Yee, {Ae Ja}",
booktitle = "Analytic and Combinatorial Number Theory",
address = "United States",
}