On duplicate representations as $2^x + 3^y$ for nonnegative integers $x$ and $y$
Number Theory
2019-07-11 v2
Abstract
We prove a conjecture posted in the Online Encyclopedia of Integer Sequences, namely that there are exactly five positive integers that can be written in more than one way as the sum of a nonnegative power of 2 and a nonnegative power of 3. The case for both powers being positive follows from a theorem of Bennett. We use elementary methods to prove the case where zero exponents are allowed.
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Cite
@article{arxiv.1907.03347,
title = {On duplicate representations as $2^x + 3^y$ for nonnegative integers $x$ and $y$},
author = {Douglas Edward Iannucci},
journal= {arXiv preprint arXiv:1907.03347},
year = {2019}
}
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5 pages