Pairs of numbers x > y > 0 such that x^5 + y^5 is a square, x is as small as possible, and x/y is unique.
2, 2, 33, 22, 66, 33, 164, 41, 183, 61, 209, 152, 2305, 1844, 2665, 2460, 4210, 2526, 4774, 2046, 5068, 3801, 12922, 4473, 13097, 3742, 15630, 3126, 15785, 6314, 15864, 13881, 19434, 5530, 21258, 2362, 24211, 19809, 24893, 24211, 27755, 20069, 29128, 3641
1
As the exponent is increased, it becomes harder to find terms.
T. D. Noe, Plot of 36 terms
T. D. Noe, Table of 36 terms
(Mma) mx = 30000; s5 = {}; t5 = {}; Do[If[IntegerQ[Sqrt[a^5 + b^5]] && ! MemberQ[s5, a/b], AppendTo[s5, a/b]; AppendTo[t5, {a, b}]], {a, mx}, {b, a}]
nonn,hard
T. D. Noe, Apr 06 2017