`Chen Shuwen's Equal Sums of Like Powers Page`

Ideal non-negative integer solutions:	164 types found (2023-4-12)
Ideal integer solutions:	65 types found (2023-5-12)
Ideal prime solutions:	24 types found (2023-4-12)

1¹ + 19¹ + 20¹ + 51¹ + 57¹ + 80¹ + 82¹ = 2¹ + 12¹ + 31¹ + 40¹ + 69¹ + 71¹ + 85¹

1² + 19² + 20² + 51² + 57² + 80² + 82² = 2² + 12² + 31² + 40² + 69² + 71² + 85²

1³ + 19³ + 20³ + 51³ + 57³ + 80³ + 82³ = 2³ + 12³ + 31³ + 40³ + 69³ + 71³ + 85³

1⁴ + 19⁴ + 20⁴ + 51⁴ + 57⁴ + 80⁴ + 82⁴ = 2⁴ + 12⁴ + 31⁴ + 40⁴ + 69⁴ + 71⁴ + 85⁴

1⁵ + 19⁵ + 20⁵ + 51⁵ + 57⁵ + 80⁵ + 82⁵ = 2⁵ + 12⁵ + 31⁵ + 40⁵ + 69⁵ + 71⁵ + 85⁵

1⁶ + 19⁶ + 20⁶ + 51⁶ + 57⁶ + 80⁶ + 82⁶ = 2⁶ + 12⁶ + 31⁶ + 40⁶ + 69⁶ + 71⁶ + 85⁶

1^k + 12^k + 25^k + 66^k + 91^k + 130^k + 174^k + 213^k + 238^k + 279^k + 292^k + 303^k

= 4^k + 6^k + 31^k + 58^k + 105^k + 117^k + 187^k + 199^k + 246^k + 273^k + 298^k + 300^k

( k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 )

2589701^k + 2972741^k + 6579701^k + 9388661^k + 9420581^k + 15740741^k + 15772661^k + 18581621^k + 22188581^k + 22571621^k

= 2749301^k + 2781221^k + 6835061^k + 8399141^k + 10314341^k + 14846981^k + 16762181^k + 18326261^k + 22380101^k + 22412021^k

( Prime solution, k = 1, 2, 3, 4, 5, 6, 7, 8, 9 )

Last revised on May 12, 2023

Main site:	http://eslpower.org	(Created and maintained by Chen Shuwen )
Historical version:	http://euler.free.fr/eslp	(Courtesy of Jean-Charles Meyrignac, last updated on May 6, 2001 )

Chen Shuwen

Seekway Innovations Technology Limited,

Building 3, Qunhua Hi-Tech Park,

15#, Qunhua Road,

Jiangmen City, Guangdong Province

People's Republic of China