SOLUTION: If m,n are integers, how many solutions are there to n^2+n+1=m^3?

Question 1139563: If m,n are integers, how many solutions are there to n^2+n+1=m^3?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If m,n are integers, how many solutions are there to n^2+n+1=m^3?
:
Not counting n=0, there is only 1 solution, n = 18. m = 7
:
Well I am not too proud of the way I did it, but here is what I did
I put the equation into my Ti83, n = x, m = y, as follows
y = (x^2+x+1)^(1/3)
Then I went to the associated table and looked for integer solutions and only one came up x=18; y=7
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