Question

Find the remainder when 1x1!+2x2!+3x3!+...+250x250! is divided by 2008.

Answer 1

I wonder if this is related to modular arithmetic :/

Answer 2

Challenge accepted.

Answer 3

im getting 2007 as an answer. Can I verify this is correct before I post a solution?

Answer 4

it is correct

Answer 5

how to get it?

Answer 6

I took a little shortcut on the Chinese Remainder Theorem part, but if you didnt do it that way it would still work out.

Answer 7

thank you very much! :)

Answer 8

Well, Joe beat me to it.

The key observation is that it's a telescoping sum.