1963/03/19 by H. Davenport · 91 citations
Computer Science · Mathematics · #Polynomial and algebraic computation #Functional Equations Stability Results #Advanced Differential Equations and Dynamical Systems #Mathematics #Combinatorics #Cubic form #Statistics
paper · doi:10.1098/rspa.1963.0054
published in Proceedings of the Royal Society of London A Mathematical and Physical Sciences 272(1350), 285-303 (Royal Society)
openalex publication_date 1963/03/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21
Abstract It is proved that if C(x1, ..., xn) is any cubic form in n variables, with integral coefficients, then the equation C(x1, ..., xn) = 0 has a solution in integers x1, ..., xn not all 0, provided n is at least 16. This is an improvement upon earlier results (Davenport 1959, 1962).