Let (x1,y1,z1), (x2,y2,z2), …, (xn,yn,zn) be the rational solutions to the following system of equations
x+y+z=0x3+y3+z3=18x7+y7+z7=2058
Evaluate:
i=1∑nxiyizi
- The triple (a,b,c) and (c,a,b) are considered to be different.
- This problem is not entirely original.