Sum of 2 Lucky Numbers in 4 Ways
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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): $34$