8911

Number
$8911$ (eight thousand, nine hundred and eleven) is:


 * $7 \times 19 \times 67$


 * The $7$th Carmichael number after $561$, $1105$, $1729$, $2465$, $2821$, $6601$:
 * $\forall a \in \Z: a \perp 8911: a^{8910} \equiv 1 \pmod {8911}$


 * The $22$nd Poulet number after $341$, $561$, $645$, $1105$, $1387$, $\ldots$, $4369$, $4371$, $4681$, $5461$, $6601$, $7957$, $8321$, $8481$:
 * $2^{8911} \equiv 2 \pmod {8911}$: $8911 = 7 \times 19 \times 67$


 * The $67$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $6903$, $7140$, $7381$, $7626$, $7875$, $8128$, $8385$, $8646$:
 * $8911 = \ds \sum_{k \mathop = 1}^{67} \paren {4 k - 3} = 67 \paren {2 \times 67 - 1}$


 * The $133$rd triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $7503$, $7626$, $7750$, $7875$, $8001$, $8128$, $8256$, $8385$, $8515$, $8646$, $8778$:
 * $8911 = \ds \sum_{k \mathop = 1}^{133} k = \dfrac {133 \times \paren {133 + 1} } 2$