The special number 3,628,799

For N=1 to 10:

3,628,799/N always gives you remainder as (N-1)

3,628,799 / 1 gives you remainder 0

3,628,799 / 2 gives you remainder 1

3,628,799 / 3 gives you remainder 2

3,628,799 / 4 gives you remainder 3

3,628,799 / 5 gives you remainder 4

3,628,799 / 6 gives you remainder 5

3,628,799 / 7 gives you remainder 6

3,628,799 / 8 gives you remainder 7

3,628,799 / 9 gives you remainder 8

3,628,799 / 10 gives you remainder 9

Also for N=0 to 9:

(3,628,799-N)/(N+1) always gives you a whole number

(3,628,799-0) / 1 = 3,628,799

(3,628,799-1) / 2 = 1,814,399

(3,628,799-2) / 3 = 1,209,599

(3,628,799-3) / 4 = 907,199

(3,628,799-4) / 5 = 725,759

(3,628,799-5) / 6 = 604,799

(3,628,799-6) / 7 = 518,399

(3,628,799-7) / 8 = 453,599

(3,628,799-8) / 9 = 403,199

The trick is that $3,628,799 = 10!-1$

#NumberTheory

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Comments

I noticed the "trick" as soon as I read the name of the note as 3,628,799... :D

Syed Hamza Khalid - 2 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$