Powers of 2 which are Sum of Distinct Powers of 3

From ProofWiki
Jump to navigation Jump to search

Unproven Conjectures

The powers of $2$ which are sums of distinct powers of $3$ are:

\(\ds 2^0\) \(=\) \(\, \ds 1 \, \) \(\, \ds = \, \) \(\ds 3^0\)
\(\ds 2^2\) \(=\) \(\, \ds 4 \, \) \(\, \ds = \, \) \(\ds 3^0 + 3^1\)
\(\ds 2^8\) \(=\) \(\, \ds 256 \, \) \(\, \ds = \, \) \(\ds 3^0 + 3^1 + 3^2 + 3^5\)

It has been conjectured by Paul Erdős that there are no others.


Sources