Pairs of numbers x > y > 0 such that x^7 + y^7 is a square, x is as small as possible, and x/y is unique.
2, 2, 258, 129, 1516, 1137, 1641, 547, 6945, 4630, 7985, 3194, 34278, 5713, 52505, 42004, 65540, 16385
1
There are no other pairs with x < 100000.
T. D. Noe, Plot of 9 pairs
(Mma) mx = 10000; s7 = {}; t7 = {}; Do[If[IntegerQ[Sqrt[a^7 + b^7]] && ! MemberQ[s7, a/b], AppendTo[s7, a/b]; AppendTo[t7, {a, b}]], {a, mx}, {b, a}]
nonn,hard
T. D. Noe, Apr 06 2017