Really Hard Math Riddle?

[Alexis]

so i actually don't no the answer to this, but i need it for math extra credit so any help?

This number is between 1 and 10000. If the divide it by 10, you get a remainder of 9. If you divide it by 9, you get a remainder of 8. If you divide it by 8, you get a remainder of 7. If you divide it by 7, you get a remainder of 6. And so on until you divide it by 2 and get a remainder of 1.

plz help me!

[shhrewd]

Ah. This is a classic.
I hope you are familiar with mods. If not, here's a general idea
x = a mod b
x/b yields a remainder of a.

x = 9 mod 10 = -1 mod 10
x = 8 mod 9 = - 1 mod 9
x = 7 mod 8 = - 1 mod 8
...
x = 1 mod 2 = - 1 mod 2

Now, if we find the LCM of (2,3,4...9,10) - 1, thats our answer! =)

2520 - 1 = 2519 is our answer

[Mark]

Hint: Look up "Chinese Remainder Theorem"