# 10,000

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## Number

$10 \, 000$ (ten thousand) is:

$2^4 \times 5^4$

The $4$th power of $10$ after $(1)$, $10$, $100$, $1000$:
$10 \, 000 = 10^4$

The $10$th fourth power after $1$, $16$, $81$, $256$, $625$, $1296$, $2401$, $4096$, $6561$:
$10 \, 000 = 10 \times 10 \times 10 \times 10$

The $37$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $\ldots$, $5184$, $5776$, $6084$, $6400$, $7056$, $7744$, $8100$, $9216$, $9604$ to be the divisor sum value of some (strictly) positive integer:
$10 \, 000 = \map {\sigma_1} {8743} = \map {\sigma_1} {9481}$

The $100$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $9025$, $9216$, $9409$, $9604$, $9801$:
$10 \, 000 = 100 \times 100$