Research output: Book/Report › Authored book

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

Research output: Book/Report › Authored book

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

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

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.

@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",

}

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 -