Book contents
- Frontmatter
- Contents
- Preface
- Notation
- 1 Joseph Liouville (1809–1882)
- 2 Liouville's Ideas in Number Theory
- 3 The Arithmetic Functions σk(n), σk*(n), dk, m(n) and Fk(n)
- 4 The Equation i2 + jk = n
- 5 An Identity of Liouville
- 6 A Recurrence Relation for σ*(n)
- 7 The Girard-Fermat Theorem
- 8 A Second Identity of Liouville
- 9 Sums of Two, Four and Six Squares
- 10 A Third Identity of Liouville
- 11 Jacobi's Four Squares Formula
- 12 Besge's Formula
- 13 An Identity of Huard, Ou, Spearman and Williams
- 14 Four Elementary Arithmetic Formulae
- 15 Some Twisted Convolution Sums
- 16 Sums of Two, Four, Six and Eight Triangular Numbers
- 17 Sums of integers of the form x2 + xy + y2
- 18 Representations by x2 + y2 + z2 + 2t2, x2 + y2 + 2z2 + 2t2 and x2 + 2y2 + 2z2 + 2t2
- 19 Sums of Eight and Twelve Squares
- 20 Concluding Remarks
- References
- Index
5 - An Identity of Liouville
Published online by Cambridge University Press: 05 May 2013
Book contents
- Frontmatter
- Contents
- Preface
- Notation
- 1 Joseph Liouville (1809–1882)
- 2 Liouville's Ideas in Number Theory
- 3 The Arithmetic Functions σk(n), σk*(n), dk, m(n) and Fk(n)
- 4 The Equation i2 + jk = n
- 5 An Identity of Liouville
- 6 A Recurrence Relation for σ*(n)
- 7 The Girard-Fermat Theorem
- 8 A Second Identity of Liouville
- 9 Sums of Two, Four and Six Squares
- 10 A Third Identity of Liouville
- 11 Jacobi's Four Squares Formula
- 12 Besge's Formula
- 13 An Identity of Huard, Ou, Spearman and Williams
- 14 Four Elementary Arithmetic Formulae
- 15 Some Twisted Convolution Sums
- 16 Sums of Two, Four, Six and Eight Triangular Numbers
- 17 Sums of integers of the form x2 + xy + y2
- 18 Representations by x2 + y2 + z2 + 2t2, x2 + y2 + 2z2 + 2t2 and x2 + 2y2 + 2z2 + 2t2
- 19 Sums of Eight and Twelve Squares
- 20 Concluding Remarks
- References
- Index
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- Number Theory in the Spirit of Liouville , pp. 48 - 53Publisher: Cambridge University PressPrint publication year: 2010