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On Sums of Sixteen Biquadrates (Mémoires de la Société Mathématique de France 100)

Research output: Book/ReportAuthored book

Standard

On Sums of Sixteen Biquadrates (Mémoires de la Société Mathématique de France 100). / Deshouillers, JM; Kawada, K; Wooley, TD.

Société Mathématique de France, 2005. 117 p.

Research output: Book/ReportAuthored book

Harvard

Deshouillers, JM, Kawada, K & Wooley, TD 2005, On Sums of Sixteen Biquadrates (Mémoires de la Société Mathématique de France 100). Société Mathématique de France.

APA

Deshouillers, JM., Kawada, K., & Wooley, TD. (2005). On Sums of Sixteen Biquadrates (Mémoires de la Société Mathématique de France 100). Société Mathématique de France.

Vancouver

Deshouillers JM, Kawada K, Wooley TD. On Sums of Sixteen Biquadrates (Mémoires de la Société Mathématique de France 100). Société Mathématique de France, 2005. 117 p.

Author

Deshouillers, JM ; Kawada, K ; Wooley, TD. / On Sums of Sixteen Biquadrates (Mémoires de la Société Mathématique de France 100). Société Mathématique de France, 2005. 117 p.

Bibtex

@book{b556749dc7df43cfacffba40ec572491,
title = "On Sums of Sixteen Biquadrates (M{\'e}moires de la Soci{\'e}t{\'e} Math{\'e}matique de France 100)",
abstract = "By 1939 it was known that 13,792 cannot be expressed as a sum of sixteen biquadrates (folklore), that there exist infinitely many natural numbers which cannot be written as sums of fifteen biquadrates (Kempner) and that every sufficiently large integer is a sum of sixteen biquadrates (Davenport). In this memoir it is shown that every integer larger than $10^{216}$ and not divisible by 16 can be represented as a sum of sixteen biquadrates. Combined with a numerical study by Deshouillers, Hennecart and Landreau, this result implies that every integer larger than 13,792 is a sum of sixteen biquadrates.",
author = "JM Deshouillers and K Kawada and TD Wooley",
note = "Other identifier: 9782856291719 Other: Series ISSN: 0249-633X",
year = "2005",
language = "English",
isbn = "2856291716",
publisher = "Soci{\'e}t{\'e} Math{\'e}matique de France",
address = "France",

}

RIS - suitable for import to EndNote

TY - BOOK

T1 - On Sums of Sixteen Biquadrates (Mémoires de la Société Mathématique de France 100)

AU - Deshouillers,JM

AU - Kawada,K

AU - Wooley,TD

N1 - Other identifier: 9782856291719 Other: Series ISSN: 0249-633X

PY - 2005

Y1 - 2005

N2 - By 1939 it was known that 13,792 cannot be expressed as a sum of sixteen biquadrates (folklore), that there exist infinitely many natural numbers which cannot be written as sums of fifteen biquadrates (Kempner) and that every sufficiently large integer is a sum of sixteen biquadrates (Davenport). In this memoir it is shown that every integer larger than $10^{216}$ and not divisible by 16 can be represented as a sum of sixteen biquadrates. Combined with a numerical study by Deshouillers, Hennecart and Landreau, this result implies that every integer larger than 13,792 is a sum of sixteen biquadrates.

AB - By 1939 it was known that 13,792 cannot be expressed as a sum of sixteen biquadrates (folklore), that there exist infinitely many natural numbers which cannot be written as sums of fifteen biquadrates (Kempner) and that every sufficiently large integer is a sum of sixteen biquadrates (Davenport). In this memoir it is shown that every integer larger than $10^{216}$ and not divisible by 16 can be represented as a sum of sixteen biquadrates. Combined with a numerical study by Deshouillers, Hennecart and Landreau, this result implies that every integer larger than 13,792 is a sum of sixteen biquadrates.

M3 - Authored book

SN - 2856291716

BT - On Sums of Sixteen Biquadrates (Mémoires de la Société Mathématique de France 100)

PB - Société Mathématique de France

ER -