Cube Sequences
13=1 13+23=9 = 32 13+23+33=36 = 62 13+23+33+43=100 = 102 13+23+33+43+53=225 = 152 …. 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16…. These are triangular numbers are in bold: 1+2 =3 1+2+3=6 1+2+3+4=10 ( n(n+1)/2 )2= n2(n+1)2/4 A question I have in my mind is that Fermat’s last theorem states: If an integer n is greater than 2, then the equation an + bn = cn has no solutions in non-zero integers a, b, and c. But how about a3 + b3 + c3 = d3 … Are there any integer solutions to this? I ask this because geometrically speaking volume is 1 degree of freedom more than Read more…