When is the following fraction an integer $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$ where $a,b,c \in Z$\mathbb{Z}$?

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asked Jan 25, 2018 at 6:11

mojojojo

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When is the following fraction an integer $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$ where $a,b,c \in Z$?

I'm trying to evaluate the following fraction $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$, but I'm getting stuck using gcd arguments or divisibility arguments. This is part of an ongoing research I'm helping a professor with within the number theory department.

Note: $a,b,c \in Z$

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When is the following fraction an integer $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$ where $a,b,c \in Z$\mathbb{Z}$?

When is the following fraction an integer $\frac{3^a}{2^b-3}[(\frac{2^b}{3})^c - 1]$ where $a,b,c \in Z$?