jmc

Question

For each positive integer n, let n! denote the product 1 2 3,, (n-1) n. What is the remainder when 9! is divided by 11?

Accepted Answer

It is easy to bash this out. Otherwise the following clever observation can be made: align* &~ 1 2 3 4 5 6 7 8 9 =&~ 1(2 6)(3 4)(5 9)(7 8) =&~ 1 12 12 45 56 &~ 1 1 1 1 1 11 =&~ 1. align*