990

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Number

$990$ (nine hundred and ninety) is:

$2 \times 3^2 \times 5 \times 11$

The second of the $4$th pair of triangular numbers whose sum and difference are also both triangular:

$780 = T_{39}$, $990 = T_{44}$, $780 + 990 = T_{59}$, $990 - 780 = T_{20}$

The $4$th triangular number after $6$, $120$, $210$ which can be expressed as the product of $3$ consecutive integers:

$990 = T_{44} = 9 \times 10 \times 11$

The $44$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $496$, $528$, $561$, $595$, $630$, $666$, $703$, $741$, $780$, $820$, $861$, $903$, $946$:

$990 = \ds \sum_{k \mathop = 1}^{44} k = \dfrac {44 \times \paren {44 + 1} } 2$

Also see

• Previous  ... Next: Triangular Numbers which are Product of 3 Consecutive Integers
• Previous  ... Next: Triangular Number Pairs with Triangular Sum and Difference
• Previous  ... Next: Triangular Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $780$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $780$