n^2=a^2+b^2-1

王守恩

\(n=a^2+b^2-c^3\) ——n 能跑遍所有自然数吗？——可有通项公式？

{{n -> 0, a -> 2, b -> 2, c -> 2}}, {{n -> 1, a -> 7,  b -> 4,  c -> 4}}, {{n -> 2, a -> 5, b -> 2, c -> 3}}, {{n -> 3, a -> 8, b -> 8, c -> 5}}, {{n -> 4, a -> 8, b -> 2, c -> 4}},
{{n -> 5, a -> 3, b -> 2, c -> 2}}, {{n -> 6, a -> 18, b -> 5, c -> 7}}, {{n -> 7, a -> 2, b -> 2, c -> 1}}, {{n -> 8, a -> 6, b -> 6, c -> 4}}, {{n -> 9, a -> 8, b -> 3, c -> 4}},
{{n -> 10, a -> 3, b -> 3, c -> 2}},{{n -> 11,a -> 10, b -> 6, c -> 5}}, {{n -> 12, a -> 3, b -> 2, c -> 1}},{{n ->13, a -> 6, b -> 2, c -> 3}}, {{n ->14, a -> 5, b -> 4, c -> 3}},
{{n -> 15, a ->35,b ->11,c ->11}}, {{n -> 16, a -> 8, b -> 4, c -> 4}}, {{n -> 17, a -> 3, b -> 3, c -> 1}},{{n ->18, a -> 6, b -> 3, c -> 3}}, {{n ->19, a -> 4, b -> 2, c -> 1}},
{{n -> 20, a -> 9, b -> 8, c -> 5}}, {{n -> 21, a -> 5, b -> 2, c -> 2}}, {{n -> 22, a ->14, b ->13, c ->7}}, {{n ->23, a -> 5, b -> 5, c -> 3}}, {{n -> 24, a -> 4, b -> 3, c -> 1}},
{{n -> 25, a -> 6, b -> 4, c -> 3}}, {{n -> 26, a -> 7, b -> 2, c -> 3}}, {{n -> 27, a ->17, b -> 9, c -> 7}}, {{n -> 28, a -> 5, b -> 2, c -> 1}}, {{n ->29, a ->14, b -> 7, c -> 6}},
{{n -> 30, a ->18, b -> 7, c -> 7}}, {{n -> 31, a -> 7, b -> 3, c -> 3}}, {{n -> 32, a -> 6, b -> 2, c -> 2}}, {{n -> 33, a -> 5, b -> 3, c -> 1}}, {{n -> 34, a -> 6, b -> 5, c -> 3}},
{{n -> 35, a ->12, b -> 4, c -> 5}}, {{n -> 36, a -> 8, b -> 6, c -> 4}}, {{n -> 37, a -> 6, b -> 3, c -> 2}}, {{n -> 38, a -> 7, b -> 4, c -> 3}}, {{n -> 39, a -> 6, b -> 2, c -> 1}},
{{n -> 40, a -> 5, b -> 4, c -> 1}}, {{n -> 41, a -> 8, b -> 2, c -> 3}}, {{n -> 42, a -> 5, b -> 5, c -> 2}}, {{n -> 43, a -> 19, b ->5, c -> 7}}, {{n -> 44, a -> 6, b -> 3, c -> 1}},
{{n -> 45, a -> 7, b -> 2, c -> 2}}, {{n -> 46, a -> 8, b -> 3, c -> 3}}, {{n -> 47, a -> 7, b -> 5, c -> 3}}, {{n -> 48, a -> 13, b -> 2, c ->5}}, {{n -> 49, a -> 5, b -> 5, c -> 1}},
{{n -> 50, a -> 7, b -> 3, c -> 2}}, {{n -> 51, a -> 6, b -> 4, c -> 1}}, {{n -> 52, a -> 7, b -> 2, c -> 1}}, {{n -> 53, a -> 8, b -> 4, c -> 3}}, {{n -> 54, a ->19, b -> 6, c -> 7}},
{{n -> 55, a ->12, b -> 6, c -> 5}}, {{n ->56, a ->10, b -> 9, c -> 5}}, {{n -> 57, a -> 7, b -> 3, c -> 1}}, {{n -> 58, a -> 9, b -> 2, c -> 3}}, {{n -> 59, a ->28, b -> 2, c -> 9}},
{{n -> 60, a -> 8, b -> 2, c -> 2}}, {{n -> 61, a ->11, b -> 2, c -> 4}}, {{n -> 62, a -> 8, b -> 5, c -> 3}}, {{n -> 63, a -> 9, b -> 3, c -> 3}}, {{n -> 64, a -> 6, b -> 6, c -> 2}},
{{n -> 65, a -> 8, b -> 3, c -> 2}}, {{n -> 66, a -> 7, b -> 5, c -> 2}}, {{n -> 67, a -> 8, b -> 2, c -> 1}}, {{n -> 68, a ->12, b -> 7, c -> 5}},{{n -> 69, a ->13, b -> 5, c -> 5}},
{{n -> 70, a -> 9, b -> 4, c -> 3}}, {{n -> 71, a -> 7, b -> 7, c -> 3}}, {{n -> 72, a -> 8, b -> 3, c -> 1}}, {{n -> 73, a -> 8, b -> 6, c -> 3}}, {{n -> 74, a -> 13, b ->11, c -> 6}},
{{n -> 75, a -> 14, b -> 2, c -> 5}},{{n ->76, a -> 16, b -> 6, c -> 6}},{{n -> 77, a -> 9, b -> 2, c -> 2}}, {{n -> 78, a ->15, b ->14, c ->7}}, {{n -> 79,  a -> 9, b -> 5, c -> 3}},
{{n -> 80, a -> 14, b -> 3, c -> 5}}, {{n -> 81, a -> 8, b -> 5, c -> 2}}, {{n -> 82, a -> 9, b -> 3, c -> 2}}, {{n -> 83, a -> 12, b -> 8, c -> 5}}, {{n -> 84, a -> 9, b -> 2, c -> 1}},
{{n -> 85, a -> 10, b -> 7, c -> 4}}, {{n -> 86, a -> 8, b -> 7, c -> 3}}, {{n -> 87, a -> 14, b -> 4, c -> 5}}, {{n -> 88, a -> 8, b -> 5, c -> 1}}, {{n -> 89, a -> 9, b -> 3, c -> 1}},
{{n -> 90, a ->  9,  b -> 6, c -> 3}}, {{n -> 91, a ->28, b -> 6, c -> 9}}, {{n -> 92, a -> 8, b -> 6, c -> 2}}, {{n -> 93, a -> 13, b -> 7, c -> 5}},{{n ->94, a ->45, b ->38, c ->15}},
{{n -> 95, a -> 11, b -> 1, c -> 3}}, {{n -> 96, a ->10, b -> 2, c -> 2}}, {{n -> 97, a -> 7, b -> 7, c -> 1}}, {{n -> 98, a -> 11, b -> 2, c -> 3}}, {{n -> 99, a -> 8, b -> 6, c -> 1}},

更——   \(n=a^2+b^2-c^4\)   ——n 能跑遍所有自然数吗？