(most elegant) solution of equation

JeffM said:
Leave it to you to find computationally all the solutions to the original problem. But I think at the end of the day the OP wanted a generic solution to a family of problems. The whole thing would have been more interesting had the OP put more constraints on the problem.
Click to expand...

Yes, I was looking for a (same) family of solutions for a family of problems. Such a family of solutions should be such that, on basis of it, a solution to any of the aforementioned equations --and also to the following ones, and many others (you can guess the pattern)-- could be provided, with no calculus at all:

a+16b+81c+256d+625e+1296f=0
a+16b+81c+256d+625e+1296f+2401g=0
a+16b+81c+256d+625e+1296f+2401g+4096h=0
... and so on
 
ednoc said:
Yes, I was looking for a (same) family of solutions for a family of problems. Such a family of solutions should be such that, on basis of it, a solution to any of the aforementioned equations --and also to the following ones, and many others (you can guess the pattern)-- could be provided, with no calculus at all:

a+16b+81c+256d+625e+1296f=0
a+16b+81c+256d+625e+1296f+2401g=0
a+16b+81c+256d+625e+1296f+2401g+4096h=0
... and so on
Click to expand...
I answered your qustion in post # 16.
 
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