Equal Sums of Like Powers

What is New on This Site

• Equal sums of like powers is revised.
• T/L = 94 types ( m = n + 1, non-negative integers)
• Unsolved problems and conjectures
• Question I by Chen Shuwen and Conjectures by Chen Shuwen are modified.
• A new page is added: Multigrade Chains.
• T/L = 10 types ( m = n + 1, j>=3, non-negative integers)
• T/L = 7 types ( m = n + 1, any j, non-negative integers)
• T/L = 2 types ( m = n , j>=3, integers)
• A new page is added: Results and discussion on the k < 0 case.
• First known solution of ( k = -1, 1).
• A new page is added: ( k = -1, 1).

• Equal sums of like powers is revised. ( Only consider k > 0 in the page.)
• Records on equal sums of like powers
• T/L = 39 types ( m = n + 1, k > 0, non-negative integers)
• T/L = 13 types ( m = n, h > 0, integers)
• Equal Products and Equal sums of like powers
• Frist solution for ( k = 0, 1, 2, 3 ) by Quo Xianqiang.

• The main site is moved to: http://go6.163.com/~eslp (Redirect URL: http://eslp.yeah.net )
• A new page is added: Equal Products and Equal sums of like powers
• First solution for ( k = 0 ), ( k = 0, 1 ), ( k = 0, 1 ), ( k = 0, 2 ), ( k = 0, 1, 2 ) and ( h = 0, 1, 3 )
• Frist solution for ( k = 0, 1, 2, 3 ), ( k = 0, 1, 2, 3, 4 ), ( k = 0, 1, 2, 3, 4, 5 ), ( k = 0, 1, 2, 3, 4, 5, 6 )
• Records on equal sums of like powers
• T/L =47 types (m=n+1, non-negative integers)
• T/L =14 types (m=n, integers)
• Equal sums of like powers is revised.
• New solution for ( h = 1, 2, 6 ) by Ajai Choudhry
• All the pages have been modified.

• First solution for ( k = 1, 3, 7 ) by Ajai Choudhry in 1999.
• Equal sums of like powers is revised.
• Thanks for Jean-Charles Meyrignac mirror this site: http://euler.free.fr/eslp
• Records on equal sums of like powers
• T/L =39 types (m=n+1, non-negative integers)
• T/L =13 types (m=n, integers)

• First solution for ( k = 1, 3, 5, 7, 9 ) by Chen Shuwen
• First solution for ( h = 1, 2, 3, 5, 7, 9 ) by Chen Shuwen
• New solution for ( k = 2, 4, 6, 8 )
• New solution for ( k = 1, 2, 3, 4, 5, 6, 7, 8, 9 )
• Records on equal sums of like powers
• T/L =39 types (m=n+1, non-negative integers)
• T/L =13 types (m=n, integers)

• First solution for ( h = 1, 3, 4 ) by Ajai Choudhry
• Records on equal sums of like powers
• T/L =38 types (m=n+1, non-negative integers)
• T/L =12 types (m=n, integers)

• First solution for ( k = 1, 3, 7 )
• Records on equal sums of like powers
• T/L =38 types (m=n+1, non-negative integers)
• T/L =11 types (m=n, integers)

• First solution for ( h = 1, 2, 4, 6, 8, 10 )
• Records on equal sums of like powers
• T/L =37 types (m=n+1, non-negative integers)
• T/L =11 types (m=n, integers)

• First solution for ( k = 2, 4, 6, 8, 10 )
• First solution for ( k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 )
• Records on equal sums of like powers
• T/L =37 types.
• The Prouhet-Tarry-Escott problem
• Great progress on ( k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 )
• Unsolved problems and conjectures

• First solution for ( k = 1, 2, 3, 5, 7 ) 
• Records on equal sums of like powers
• T/L =35 types.
• Non-negative integer solutions of the m=n+2 case
• ( k = 2, 4, 8 ) by Randy L. Ekl
• Other results on equal sums of like powers
• A link to Jean-Charles Meyrignac's site
• Discussion and comments
• Some E-mails about Equal sums of likes recently.

• First solution for ( k = 1, 2, 3, 6 ) 
• First solution for ( k = 1, 2, 3, 4, 5, 6, 8 ) 
• Records on equal sums of like powers
• New solutions on ( k = 1, 2, 3, 4, 5, 7 ) 
• Internet resources collection

• Internet resources collection
• Discussion and comments

• Chen's Equal sums of like powers site is moved to http://www.nease.net/~chin/eslp.
• Discussion and comments
• Some E-mails sent to Chen during Auget 1 to December 31, 1997.
• A new solution of ( 4, 1, 3 ) by Allan MacLeod.
• Sign gusetbook and View Guestbook
• Internet resources collection
• Wide Area Distributed Computation: The Prouhet-Tarry-Escott Problem

• Internet resources collection
• Sums of square roots ( An application of the Prouhet-Tarry-Escott problem ).
• Unsolved problems and conjectures
• P.Borwein and C.Ingalls had found and proved the ( k = 1, 2, ..., n ) case of Conjecture II in 1994.
• Discussion and comments
• Some E-mails sent to Chen during July 13 to Auget 1.
• References
• [59] is added.

• Other results on equal sums of like powers
• The first solution of the type ( 5, 2, 3 ) is known.
• Internet resources collection
• Some new resources are added to this collection page.
• Unsolved problems and conjectures
• The first version of this page is finished.
• Discussion and comments
• E-mails sent to Chen discussing the topic " Equal sums of like powers" or commenting on Chen's site.
• References
• [48]~[58] and "Other References" are added.
• What is new
• This page is added for the first time.
• ( k = 1, 4 )
• Chen Shuwen obtained a parametric solution of this type in July 1997.

• Chen Shuwen's Euqal Sums of Like Powers site is published.