I don't normally post on /sci/ but there is a problem which has been bugging me. Can you prove that there is / isn't a solution to this problem where n is a natural number and x is a rational number where 0 < x < 1? It seems like it should be possible to prove one way or the other, but I can't think of how to approach it.
Also, there is no solution, then I have a follow up question about a similar formula:
a = (1 + x)^n
with the same constraints, but "a" is also a natural number?