Triangular Number Pairs with Triangular Sum and Difference/Examples/T14, T18
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Example of Triangular Number Pair with Triangular Sum and Difference
The triangular numbers $T_{14}$ and $T_{18}$ have sum and difference which are themselves both triangular:
| \(\ds T_{14}\) | \(=\) | \(\ds \frac {14 \times 15} 2\) | $= 105$ | |||||||||||
| \(\ds T_{18}\) | \(=\) | \(\ds \frac {18 \times 19} 2\) | $= 171$ |
| \(\ds T_{18} - T_{14}\) | \(=\) | \(\ds 171 - 105\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 66\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {11 \times 12} 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds T_{11}\) |
| \(\ds T_{18} + T_{14}\) | \(=\) | \(\ds 171 + 105\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 276\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {23 \times 24} 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds T_{23}\) |
$\blacksquare$