Triangular Number Pairs with Triangular Sum and Difference/Examples/T1869, T2090
Jump to navigation
Jump to search
Example of Triangular Number Pair with Triangular Sum and Difference
The triangular numbers $T_{1869}$ and $T_{2090}$ have sum and difference which are themselves both triangular:
| \(\ds T_{1869}\) | \(=\) | \(\ds \frac {1869 \times 1870} 2\) | \(\ds = 1 \, 747 \, 515\) | |||||||||||
| \(\ds T_{2090}\) | \(=\) | \(\ds \frac {2090 \times 2091} 2\) | \(\ds = 2 \, 185 \, 095\) |
| \(\ds T_{2090} - T_{1869}\) | \(=\) | \(\ds 2 \, 185 \, 095 - 1 \, 747 \, 515\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 437 \, 580\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {935 \times 936} 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds T_{935}\) |
| \(\ds T_{2090} + T_{1869}\) | \(=\) | \(\ds 2 \, 185 \, 095 - 1 \, 747 \, 515\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 3 \, 932 \, 610\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {2804 \times 2805} 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds T_{2804}\) |
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1,747,515$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,747,515$