Sum of 3 Squares in 2 Distinct Ways
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Theorem
$27$ is the smallest positive integer which can be expressed as the sum of $3$ square numbers in $2$ distinct ways:
| \(\ds 27\) | \(=\) | \(\ds 3^2 + 3^2 + 3^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 5^2 + 1^2 + 1^2\) |
Proof
Can be performed by brute-force investigation.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $27$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $27$