(In reply to
Solution by Brian Smith)
Great solution. I doubt I ever would have found it.
I jotted this problem down to work on away from my computers and left out nonnegative. I started searching for these negatives on my calculator and got stuck down the rabbit hole of complex conjugates not realizing the solutions were all going to be rational.
If we don't restrict R, there are an infinite number of solutions, but the rest are negative:
I=5 R=14812/125
I=6 R=734174/729
I=7 R=30289904/21^3
etc.
(I was logging in to share my approximate solutions but now I don't need to.)

Posted by Jer
on 20160709 13:50:28 