Sum of 3 Squares in 2 Distinct Ways

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): $27$
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