Sums of Partial Sequences of Squares/Examples
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Examples of Sums of Partial Sequences of Squares
Example: $3^2 = 4 + 5$
| \(\ds 3\) | \(=\) | \(\ds 1 + 2\) | ||||||||||||
| \(\ds 3^2\) | \(=\) | \(\ds 4 + 5\) | ||||||||||||
| \(\ds 3^2 + 4^2\) | \(=\) | \(\ds 5^2\) |
Example: $5^2 = 12 + 13$
| \(\ds 5\) | \(=\) | \(\ds 2 + 3\) | ||||||||||||
| \(\ds 5^2\) | \(=\) | \(\ds 12 + 13\) | ||||||||||||
| \(\ds 10^2 + 11^2 + 12^2\) | \(=\) | \(\ds 13^2+ 14^2\) |
Example: $7^2 = 24 + 25$
| \(\ds 7\) | \(=\) | \(\ds 3 + 4\) | ||||||||||||
| \(\ds 7^2\) | \(=\) | \(\ds 24 + 25\) | ||||||||||||
| \(\ds 21^2 + 22^2 + 23^2 + 24^2\) | \(=\) | \(\ds 25^2 + 26^2 + 27^2\) |
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $25$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $25$