A103156 Numbers whose square can be expressed as the signed sum of a fifth power and a cube: z^2 = x^5 + y^3 with gcd(x,y,z)=1.

3, 10, 411, 654, 7792, 36599, 39151, 647992, 1506463, 1525899, 2730128, 3353687, 4387861, 4942947, 5574720, 12092581, 128301258, 168454745, 184589480, 888155653, 20364997771, 53242416249, 65464918703, 73699708330, 74330984303

Offset: 1

Author

Hugo Pfoertner, Jan 25 2005

Keywords

• nonn

Examples

			a(1)=3 because 1^5 + 2^3 = 3^2;
a(2)=10 because (-3)^5 + 7^3 = 10^2;
a(3)=411 because 10^5 + 41^3 = 411^2;
a(4)=654 because 19^5 + (-127)^3 = 654^2.
		

Links

• Dario Alpern, Sum of powers a^5 + b^3 = c^2.
• Johnny Edwards, A Complete Solution to X^2+Y^3+Z^5=0. Journal für die reine und angewandte Mathematik (Crelle's Journal) 571, 213-236 (2004).

Crossrefs

Cf. A070065 positive integer solutions of x^2 + y^5 = z^3.