Equal Sums of Like Powers

Non-negative Integer Solutions of

• 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.
• 698⁷ + 556⁷ + 443⁷ + 184⁷ =673⁷ + 625⁷ + 353⁷ + 230⁷
• 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)