- Ajai Choudhry
obtained solutions of this system in early 1999
`[60]`. Here is one of the numerical solution: - [ 1741, 2435, 3004, 3476 ] = [ 1937, 2111, 3280, 3328 ]
- See also Equal Sums of Seventh Powers.
- Two methods are sucessfully used almost at the same time in Sep1999. One is programmed by Jean-Charles Meyrignac, search by Nuutti Kuosa, and noticed by Chen Shuwen. Another is by Chen Shuwen. Both obtained the following smallest result of this type.
- [ 184, 443, 556, 698 ] = [ 230, 353, 625, 673 ]
- Chen Shuwen wrote a program which can search all the solutions of ( k = 1, 3, 7 ) in a certain range and discovered the above solution in 10 Sep1999 after a Pentium 100M running 68 hours. Then, Chen Shuwen found that Nuutti Kuosa had obtained the following result in 8 Sep1999 by using a program that Jean-Charles Meyrignac wrote. Jean-Charles Meyrignac's program can search all the solutions of ( 7, 4, 4 ) in a certain range.
- 698
^{7 }+ 556^{7 }+ 443^{7 }+ 184^{7 }=673^{7 }+ 625^{7 }+ 353^{7 }+ 230^{7} - Please visit Computing Minimal Equal Sums Of Like Powers for detail.
- Comparison of the two methods for ( k = 1, 3, 7 )

Jean-Charles Meyrignac's Methods |
Chen Shuwen's Methods |

Searched by Nuutti Kuosa, noticed by Chen Shuwen | Searched by Chen Shuwen |

Found solution in 10 Sep1999 | Found solution in 10 Sep1999 |

Can search all solutions of (7,4,4), include ( k=1,3,7 ) | Only can search all solutions of ( k=1,3,7 ) |

CPU: PIII-450MHz, RAM: 768 MB | CPU: PI-100MHz, RAM: 24MB |

Program language: ASM | Program language: VB 5.0 |

Computing time: 3 days? ( Range: 1 to 698) | Computing time: 68hours ( Range: 1 to 698) |

Computing speed: 1162sec ( Range: 698 to 698) | Computing speed: 1696sec ( Range: 698 to 698) |

Copyright 1997-2001, Chen Shuwen