Non-negative Integer
Solutions of
a1k
+ a2k + a3k +
a4k + a5k +
a6k + a7k
= b1k
+ b2k + b3k
+ b4k + b5k
+ b6k + b7k
( k = 1, 2, 3, 5, 7, 9 )
- Chen Shuwen obtained the
first known solution for ( k = 1, 2, 3, 5, 7, 9 ) in 27 Jan 2023.
- [ 7, 89, 91, 251, 253, 341, 373 ] = [ 29, 31, 151, 193, 311, 313, 377 ]
- By computer searching, Chen Shuwen proved that it is the smallest
solution.
- [ 269, 397, 409, 683, 743, 901, 923 ] = [ 299, 313,
493, 613, 827, 839, 941 ]
- Second known solution, by Chen Shuwen in 6 Mar 2023.
- Summaries on the ( k = 1, 2, 3, 5, ..., 2n-1, 2n+1 ) Series :
- [ 15, 25, 55, 55, 73] = [ 13, 31, 43, 67, 69
]
( k = 1, 2, 3, 5 )
- First known solution, by Chen Shuwen in 1995.
- [ 87, 233, 264, 396, 496, 540 ] = [ 90, 206,
309, 366, 522, 523 ]
( k = 1, 2, 3, 5, 7 )
- First known solution, by Chen Shuwen in 1999.
- [ 7, 89, 91, 251, 253, 341, 373 ] = [ 29, 31, 151, 193, 311, 313, 377 ]
( k = 1, 2, 3, 5, 7, 9 )
- First known solution, smallest solution, by Chen Shuwen in 2023.
Non-negative Integer
Solutions of
a1k
+ a2k + a3k +
a4k + a5k +
a6k + a7k
= b1k
+ b2k + b3k
+ b4k + b5k
+ b6k + b7k
( k = -9, -7, -5, -3, -2, -1 )
- Based on the above first solution of
( k = 1, 2, 3, 5, 7, 9 ) and Theorem 9, Chen Shuwen
obtained the first solution of ( k = -9, -7, -5, -3, -2, -1 ) in 27 Jan 2023.
- [ 1297752271862287613603, 1563107368984288914787, 1573159506405409743821, 2534987598404572177867, 3240083486702532651181, 15782342144905884849301,
16870779534209738976839 ] = [ 1311669186305851019647, 1434758376809625895391, 1933804768743408815527, 1949213571681603308081, 5376402269143762970641, 5497220297663847531779,
69893229498868918618333 ]
Last revised April 16, 2023.
Copyright 1997-2023, Chen Shuwen