Chen Shuwen's Equal Sums of Like Powers Page

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

 

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

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

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

 

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

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

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

 

14564172k + 14861400k + 18205215k + 23490600k + 34676600k + 60684050k + 42736200k + 364104300k

 = 14278600k + 15493800k + 17338300k + 26007450k + 30342025k + 72820860k + 145641720k + 728208600k

( k = -1, -2, -3, -4, -5, -6, -7 )

  

On the ideal solutions of Equal Sums of Like Powers and The Prouhet-Tarry-Escott Problem


Last revised on Oct 15, 2016.

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Historical version:  

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 (Courtesy of Jean-Charles Meyrignac, last updated on May 6, 2001 )

 

 
Chen Shuwen
Seekway Technology Limited,
Building 3, Qunhua Hi-Tech Park,
15#, Qunhua Road,
Jiangmen City, Guangdong Province
People's Republic of China
 
Email: Chen.Shuwen@eslpower.org
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