Sum of 2 Lucky Numbers in 4 Ways

Theorem

The number $34$ is the smallest positive integer to be the sum of $2$ lucky numbers in $4$ different ways.


Proof

The sequence of lucky numbers begins:

$1, 3, 7, 9, 13, 15, 21, 25, 31, 33, \ldots$

Thus we have:

\(\ds 34\) \(=\) \(\ds 1 + 33\)
\(\ds \) \(=\) \(\ds 3 + 31\)
\(\ds \) \(=\) \(\ds 9 + 25\)
\(\ds \) \(=\) \(\ds 13 + 21\)

$\blacksquare$


Sources

  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $34$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.