Powers of 2 which are Sum of Distinct Powers of 3
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
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $256$