A116145 Squares that are equal to the sum of 5 consecutive cubes.

0, 100, 225, 99225, 4708900, 8643600

Offset: 1

Author

Zak Seidov, Apr 14 2007

Keywords

• fini
• nonn
• full

Comments

m^3+(m+1)^3+(m+2)^3+(m+3)^3+(m+4)^3=5*(2+m)*(10+4*m+m^2). Corresponding values of m are -2,0,1,25,96,118.

Using the theory of elliptic curves one can show that there are no other terms. - Jaap Spies, May 28 2007

Crossrefs

Cf. A024670, A027602, A027604, A116108.

Programs

Mathematica

Select[Table[n^3 +(n+1)^3 +(n+2)^3 +(n+3)^3 +(n+4)^3, {n, -2, 1000}] ,IntegerQ[Sqrt[#]]&] (* James C. McMahon, Aug 18 2024 *)