What is New on This Site
May 12, 2023
Apr 30, 2023

Equal sums of like powers /
Equal products
and equal sums of like powers /
Ideal positive integer solutions (k<0)
 Records on the Generalization
of ProuhetTarryEscott Problem
 Ideal nonnegative integer solutions for
( k = 1, 2, 3, 5, 7, 9 ),
( k = 9, 7, 5, 3, 2, 1),
( k = 0, 1, 2, 4, 6, 8 ),
( k = 8, 6, 4, 2, 1, 0 ), ( k = 0, 1, 2,
3, 4, 5, 6, 7 ), ( k = 7 ,6, 5, 4, 3, 2,
1, 0) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 42 +
42 + 24 +
23 + 33 =
164
types are solved.
 Ideal prime solution for ( k
= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11) is found by Jaroslaw
Wroblewski.
 Ideal prime solutions:
24 types are solved.
Dec 29, 2022

Equal sums of like powers /
Equal products
and equal sums of like powers /
Ideal positive integer solutions (k<0)
 Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k
= 1, 2, 3, 7 ), ( k =
7, 3, 2, 1 ),(
k = 1, 2, 3, 4, 7 ), (
k = 7, 4, 3, 2, 1 ),
( k = 1, 1, 2, 3 ),
( k = 3, 2, 1, 1 ),
( k = 0, 2, 3 ), ( k = 3, 2,
0 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 41 +
41 + 22 +
21 + 33 = 158
types are solved.
Aug 16, 2021
Aug 6, 2019
 Equal sums of like powers /
Ideal integer solutions (h<0) /
Records on equal sums of like powers
 Ideal integer solutions for ( h = 1, 2, 3, 4, 6, 8 ), ( h = 8, 6, 4,
3, 2, 1 ) are found by Jaroslaw Wroblewski and Chen Shuwen.
 Ideal integer solutions: 15 + 15 + 6 + 6 + 21 = 63 types are solved.
Feb 13, 2019
 Ideal integer solutions (h<0)
 Equal sums of like powers /
Records on equal sums of like powers
 Ideal integer solutions for ( h = 1, 0, 2, 4 ), ( h = 4, 2, 0, 1 ),
( h = 1, 0, 1, 2, 4 ), ( h = 4, 2, 1, 0, 1 ) are found by Chen Shuwen.
 Ideal integer solutions: 14 + 14 + 6 + 6 + 21 = 61 types are solved.
 There is no ideal nonsymmetric integer solutions of ( k
= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ) in the range of Max{a_{i},b_{i}}
<= 1100. (By Chen Shuwen)
 Algebraic Identities
( The Generalization of Ramanujan's 6108 Identity )
 Identities for ( h = 1, 0, 2, 4 )
Dec 7, 2017
Dec 4, 2017
Dec 1, 2017
May 31, 2017

Ideal positive integer solutions (k<0) /
Equal sums of like powers /
Equal products
and equal sums of like powers
 Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 2, 0, 2, 4 ), ( k
= 4, 2, 0, 2 ), ( k = 0, 1,
2, 6 ), ( k = 6, 2, 1, 0 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 21 + 20 + 31 = 150
types are solved.
May 26, 2017

Ideal positive integer solutions (k<0) /
Equal sums of like powers /
Equal products
and equal sums of like powers
 Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 1, 0, 1, 2, 4 ), ( k
= 4, 2, 1, 0, 1 ), ( k = 0, 1,
2, 3, 4, 6 ), ( k = 6, 4, 3, 2, 1, 0 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 20 + 19 + 29 = 146
types are solved.
May 21, 2017
 Ideal positive integer solutions (k<0)
/ Equal sums of like powers /
Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 1, 0, 1, 2, 3, 4 ) and ( k =
4, 3,
2, 1, 0, 1 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 19 + 18 + 27 =
142
types are solved.
May 19, 2017
May 4, 2017
April 15, 2017
 Equal products
and equal sums of like powers / Ideal positive integer solutions (k<0)
 Equal sums of like powers /
Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 0, 1, 2, 3, 5 ), ( k = 5,
3, 2, 1, 0 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 18 + 17 + 25 =
138
types are solved.
 Equal sums of like powers /
Records on equal sums of like powers
 The first prime solution founders of ( k = 1, 2 ), ( k = 1, 2, 3 ) are
comfirmed. (Thanks for Carlos Rivera's help.)
 The date for first prime solution of ( k = 1, 3, 5, 7 ) are comfirmed.(Thanks
Carlos Rivera.)
April 9, 2017
 Equal products
and equal sums of like powers /
Records on equal sums of like powers
 The first nonnegative integer solution founders of ( k = 0, 2 ), ( k =
0, 3 ), ( k = 0, 4 ) are corrected.
 Equal sums of like powers /
Records on equal sums of like powers
 The first prime solution founders of ( k = 1, 2 ), ( k = 1, 2, 3 ), ( k
= 1, 2, 3, 4, 5 ), ( k = 1, 3, 5, 7 )( k = 1, 2, 3, 4, 5, 6, 7 ) are corrected.
 Ideal integer solutions (h<0)
 Parametric ideal integer solution of
( h = 1, 1, 2, 3 )
and ( h = 1, 1, 2, 3, 4, 5 )
by A.Choudhry in 2011.
 Parametric ideal integer solution of
( h = 1, 0, 1, 3 ) and ( h =
1, 0, 1, 2, 3, 5 ) by Chen Shuwen in 2017.
April 7, 2017
 Ideal positive integer solutions (k<0)
/ Ideal integer solutions (h<0) /
Equal sums of like powers /
Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 1, 1, 5 ), ( k = 5,
1, 1 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 17 + 16 + 25 =
136
types are solved.
 Ideal integer solutions for ( h = 1, 0, 1, 5 ), ( h = 5, 1, 0,
1 ) are found by Chen Shuwen.
 Ideal integer solutions: 14 + 14 + 6 + 6 + 17 = 57 types are solved.
March 30, 2017
 Ideal positive integer solutions (k<0)
/ Equal sums of like powers /
Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 2, 1, 0, 1, 2 ), ( k = 3,
1, 0, 1, 3 ), ( k = 2, 1, 1, 2 ) and ( k = 3,
2, 1, 0, 1, 2, 3 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 17 + 16 + 23 =
134
types are solved.
March 27, 2017
 Equal products
and equal sums of like powers /
Ideal integer solutions (h<0)
 Equal sums of like powers /
Records on equal sums of like powers
 Ideal integer solutions for ( h = 1, 0, 1, 3 ), ( h = 3, 1, 0, 1 ),
( h = 1, 0, 2 ), ( h = 2, 0, 1 ), ( h = 1, 0, 1, 2, 3, 5 ), ( h = 5,
3, 2, 1, 0, 1 ) are found by Chen Shuwen.
 Ideal integer solutions: 14 + 14 + 6 + 6 + 15 = 55 types are solved.
March 26, 2017
March 25, 2017
 Ideal positive integer solutions (k<0)
/
Ideal integer solutions (h<0)
 Equal sums of like powers /
Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 1, 0, 2 ), ( k = 2,
0, 1 ), ( k = 3, 0, 3 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 17 + 16 + 19 =
130
types are solved.
 Ideal integer solutions for ( h = 2, 0, 1, 2 ), ( h = 2, 1, 0, 2 ) are found by Chen Shuwen.
 Ideal integer solutions: 14 + 14 + 5 + 5 + 9 = 47 types are solved.
March 24, 2017
 Equal products
and equal sums of like powers / Ideal positive integer solutions (k<0)
 Equal sums of like powers /
Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 0, 1, 4 ), ( k = 0,
1, 5 ), ( k = 4, 1, 0 ), ( k = 5,
1, 0 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 17 + 16 + 16 = 127
types are solved.
March 23, 2017
March 22, 2017

Ideal positive integer solutions (k<0) /
Equal sums of like powers /
Equal products
and equal sums of like powers
 Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 1, 0, 1, 2 ), ( k = 1,
0, 1, 3 ), ( k = 1, 0, 1, 2, 3 ),( k
= 2, 1, 0, 1 ), ( k = 3, 1, 0,1 ) , ( k = 3, 2, 1, 0,1 ), ( k = 0, 1,
2, 4 ), ( k = 4, 2, 1, ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 14 + 13 + 16 = 121
types are solved.
March 21, 2017
 Equal products
and equal sums of like powers / Ideal positive integer solutions (k<0)
/
Ideal integer solutions (h<0)
 Equal sums of like powers /
Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 0, 2, 4, 6 ), ( k = 6,
4, 2, 0 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 13 + 12 + 10 = 113
types are solved.
 Ideal integer solutions for ( h = 0, 1, 2, 4, 6 ), ( h = 6, 4, 2,
1, 0 ) are found by Chen Shuwen.
 Ideal integer solutions: 14 + 14 + 5 + 5 + 7 = 45 types are solved.
March 20, 2017

Ideal positive integer solutions (k<0) /
Equal sums of like powers /
Records on equal sums of like powers
 Ideal nonnegative integer solutions for ( k = 1, 1, 2 ), ( k = 1, 1, 3 ), ( k
= 2, 1, 1 ), ( k = 3, 1, 1 ) are found by Chen Shuwen.
 Ideal nonnegative integer solutions: 39 + 39 + 12 + 11 + 10 = 111
types are solved.
March 19, 2017
 Equal sums of like powers /
Records on equal sums of like powers
 Prime solution for ( k = 1, 2, 4 ), ( k = 2, 4, 6 ), ( k = 1, 2, 3, 5 ),
( k = 1, 2, 4, 6 ) are found by Chen Shuwen.
 Ideal prime solutions: 23 types are solved.
 The first prime solution founders of ( k = 1, 2, 3 ), ( k = 1, 2, 3, 4 ), ( k =
1, 2, 3, 4, 5, 6 ) are corrected. ( Qiu Min and Wu Qiang found prime
solutions of these three types before April 2016, just five months earlier
than Chen Shuwen.)
 ( k = 1, 2, 3, 4, 6 )
 Parametric ideal nonnegative integer solution of
( k = 0, 1, 2, 3, 4 )
is found, by A.Choudhry in 2016.
 Parametric ideal nonnegative integer solution of ( k = 1, 2, 3, 4, 6 )
is found, by Chen Shuwen in 2017.
 ( k = 1, 2, 3, 4, 5, 6,
7, 8 )
 There is no new new symmetric
solution in the range of max { a_{i}, b_{i}
}< 13000. (By Chen Shuwen in 2016)
 There is no nonsymmetric
solution in the range of max { a_{i}, b_{i}
}< 310. (By Chen Shuwen in 20162017)
 ( k = 1, 3, 5, 7, 9 )
 There is no new positive integer solution in the range of Max{a_{i},b_{i}}<=5600.
 There is no ideal
symmetric nonnegative solutions of ( k
= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ) in the range of Max{a_{i},b_{i}}
<= 50000.
 ( k = 1, 2, 3, 4, 5, 6,
7, 8, 9 )
 Only one prime solution is found in the range of of { a_{i}, b_{i}
}< 100000000, by Chen Shuwen in 2016.
 ( k = 2, 4, 6, 8, 10
)
 There is no new solution in the range of of max {a_{i}, b_{i}
} <= 1800.
 Equal products
and equal sums of like powers
 Smallest solution for ( k = 0, 1, 2, 3, 4, 5, 6 )
October 17, 2016
 Equal sums of like powers /
Records on equal sums of like powers
 Prime solution for ( k = 2, 6 ) by Aloril, JeanCharles Meyrignac, Chen
Shuwen
 Ideal prime solutions: 19 types are solved.
 The first prime solution founders of ( k = 2 ), ( k = 3 ), ( k = 4 ), (
k = 1, 5 ), ( k = 1, 3, 5 ) and ( k = 1, 3, 5, 7 ) are corrected.
October 15, 2016
October 16, 2001
May 8, 2001
 Equal sums of like powers
 T/L = 105 types ( m = n + 1, nonnegative integers)
 Results and discussion on
the k < 0 case.
 First known solution of ( k = 1, 2 ) , ( k = 2, 1 ) , ( k = 1, 0,
1 )
 T/L = 4 types ( m = n + 1, k1 < 0, kn >0,
nonnegative integers)
 Equal Products and Equal
sums of like powers
 First known solution of ( k = 0, 3 ) , ( k = 0, 4 ) , ( k = 0, 1, 3
) , ( k = 0, 2, 4 )
 T/L = 12 types ( m = n + 1, k1 = 0, others k
>0, nonnegative integers)
May 6, 2001
April 2, 2001
March 31, 2001
 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, nonnegative integers)
 T/L =14 types (m=n, integers)
 Equal sums of like powers
 New solution for ( h = 1,
2, 6 ) by Ajai Choudhry
 All the pages have been modified.
February 25, 2001
October 16, 2000
 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, nonnegative integers)
 T/L =13 types (m=n, integers)
November 5, 1999
September 10, 1999
September 8, 1999
September 7, 1999
 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
 The ProuhetTarryEscott
problem
 Great progress on ( k =
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 )
 Unsolved problems and conjectures
Augest 16, 1999
July 14,1999
 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
May 9, 1998
January 18, 1998
Auget 1, 1997
July 13, 1997
June 28, 1997
Last revised on Apr
30,
2023
Copyright 19972023, Chen Shuwen