Equal Sums of Like Powers

Non-negative Integer Solutions of

• This equation was first studied by Euler. He gave a two-parameter solution in 1772.[9] Numerical example is
• [ 59, 158 ] = [ 133, 134 ]
• Lander, Parkin and Selfridge made a computer search on this type in 1960's and gave a list of 46 primitive solutions. [10] [11] Here are all the solutions in the range max { a_i, b_i }< 1000.
• [ 59, 158 ] = [ 133, 134 ]
• [ 7, 239 ] = [ 157, 227 ]
• [ 193, 292 ] = [ 256, 257 ]
• [ 271, 502 ] = [ 298, 497 ]
• [ 103, 542 ] = [ 359, 514 ]
• [ 222, 631 ] = [ 503, 558 ]
• In 1982, A.J.Zajta discussed the more important solution methods of this equation and presented a list of 218 numerical solutions.[12] This list contained all known primitive and nontrivial solutions in the range max { a_i, b_i }< 10⁶.