Equal Sums of Like Powers

Non-negative Integer Solutions of

• Solution methods on this equation can be seen in [1] [3] .Numerical exampls are
• [ 1, 12 ] = [ 9, 10 ]
• [ 2, 16 ] = [ 9, 15 ]
• [ 2, 34 ] = [ 15, 33 ]
• [ 3, 60 ] = [ 22, 59 ]
• [ 10, 27 ] = [19, 24 ]
• J.Leech obtained this solution, which is the smallest such sample. [41] [43]
• [ 167, 436 ] = [ 228, 423 ] = [ 255, 414 ]
• E.Rosenstiel, J.A.Dardis and C.R.Rosenstiel gave the four least examples of such type in 1991 by using computer.[42]
• [ 2421, 19083 ] = [ 5436, 18948 ] = [ 10200, 18072 ] = [ 13322, 16630 ]
• [ 4275, 23237 ] = [ 7068, 23066 ] = [ 10362, 22580 ] = [ 12939, 21859 ]