Pairs of numbers x > y > 0 such that x^9 + y^9 is a square, x is as small as possible, and x/y is unique.
2, 2, 114, 57, 14763, 4921, 60585, 40390
1
There are no other pairs with x < 100000.
T. D. Noe, Plot of 4 pairs
(Mma) mx = 20000; s9 = {}; t9 = {}; Do[If[IntegerQ[Sqrt[a^9 + b^9]] && ! MemberQ[s9, a/b], AppendTo[s9, a/b]; AppendTo[t9, {a, b}]], {a, mx}, {b, a}]
nonn,hard
T. D. Noe, Apr 06 2017