Equal Sums of Like Powers

Non-negative Integer Solutions of

• The first solution known for this type was due to A.Moessner in 1939. [3] [13]
• [ 39, 92, 100 ] = [ 49, 75, 107 ]
• A two parameter solution of seventh degree was found by Moessner and two parametric solutions were found by H.Swinnerton-Dyer. [14]
• L.J.Lander obtained a 3-parameter solution of this system in 1968. [14]
• L.J.Lander, T.R.Parkin and J.L.Selfridge made a computer search using CDC6600 to the following Diophantine equation in least integers
a₁⁵ + a₂⁵ + a₃⁵ = b₁⁵ + b₂⁵ + b₃⁵
They found 45 primitive solutions of which 32 solutions were also satisfy the additional condition
a₁ + a₂ + a₃ = b₁ + b₂ + b₃
Here are the primitive solutions in least integers by their computer search. [11]
• [ 13, 51, 64 ] = [ 18, 44, 66 ]
• [ 3, 54, 62 ] = [ 24, 28, 67 ]
• [ 8, 62, 68 ] = [ 21, 43, 74 ]
• [ 53, 72, 81 ] = [ 56, 67, 83 ]