Triangular Number Pairs with Triangular Sum and Difference/Examples/T27, T37
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Example of Triangular Number Pair with Triangular Sum and Difference
The triangular numbers $T_{27}$ and $T_{37}$ have sum and difference which are themselves both triangular:
| \(\ds T_{27}\) | \(=\) | \(\ds \frac {27 \times 28} 2\) | $= 378$ | |||||||||||
| \(\ds T_{37}\) | \(=\) | \(\ds \frac {37 \times 38} 2\) | $= 703$ |
| \(\ds T_{37} - T_{27}\) | \(=\) | \(\ds 703 - 378\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 325\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {25 \times 26} 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds T_{25}\) |
| \(\ds T_{37} + T_{27}\) | \(=\) | \(\ds 703 + 378\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1081\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {46 \times 47} 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds T_{46}\) |
$\blacksquare$