Given a fixed odd integer $y\in\mathbb{Z}$ and a natural number $n\in\mathbb{N}$, can we compute the cardinality of the set $\{(m,k)\in\mathbb{N}^2:k\leq n, 2^m-3^k=y\}$ explicitly?
Thanks in advance for any help.
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2Note (as in the solution to problem 1404, here: https://www.jstor.org/stable/2690747) that any $y > 8$ that is not congruent to either $5$ or $7$ mod $8$ can be immediately ruled out. – Connor Harris Apr 01 '19 at 18:21
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2Probably not..see here for the case $y=1$. – Dzoooks Apr 01 '19 at 18:23