If indeed George were mildly phobic of any quantity which is not a power of two, then cases of wine must be very tricky. This led to me wondering, what power of three is closest to a power of two, the difference being expressed as a fractional part or percentage of the power of three.winesecretary wrote: I also have acquired 4 halves, 2 bottles and 1 magnum of Niepoort.
i.e. For what x is (3^x - 2^y)/3^x minimised, for any positive (non-zero, if that needs saying) integer values of x and y?
Corollary: Intuitively, it feels that there should be no limit, with some potential huge values of x and y for which 3^x - 2^y = +/-1, but can this be proven or disproven?