Triangular Number Pairs with Triangular Sum and Difference/Examples/T39, T44
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Example of Triangular Number Pair with Triangular Sum and Difference
The triangular numbers $T_{39}$ and $T_{44}$ have sum and difference which are themselves both triangular:
| \(\ds T_{39}\) | \(=\) | \(\ds \frac {39 \times 40} 2\) | $= 780$ | |||||||||||
| \(\ds T_{44}\) | \(=\) | \(\ds \frac {44 \times 45} 2\) | $= 990$ |
| \(\ds T_{44} - T_{39}\) | \(=\) | \(\ds 990 - 780\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 210\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {20 \times 21} 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds T_{20}\) |
| \(\ds T_{44} + T_{39}\) | \(=\) | \(\ds 990 + 780\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1770\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {59 \times 60} 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds T_{59}\) |
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $780$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $780$