I am pretty sure not. But cannot yet prove it.

If you rearrange for a I think you get

If b and n are +ve integers then it is obvious that every term except

is an integer. So for a to be an integer then that term must also be an integer (ie if it is less than 1 then no matter how much you add to it - or whatever integer you divide it by it will always be less than 1. or if it is greater than 1 then it cannot be irrational for similar reasons). I feel I should be able to show that cannot be the case - but I cannot

A little learning is a dangerous thing; drink deep, or taste not the Pierian spring:

there shallow draughts intoxicate the brain, and drinking largely sobers us again.

- Alexander Pope

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