Math challenge

Is the number

2 - 2009

- 1

divided by 1155?

Show me the answer, I don't want to think

    YES, DIVIDED.
        			  
The number of the form:
(2^k) - 1 is divided by 3:
if and only if when k is even;
by 5 - when k is a multiple of 4;
by 7 - when k is a multiple of 3;
by 11 - when k is a multiple of 10;
    
Exponent of 2^2007 + 3^2008 - 2009
is divided by 4; also it is divided
by 3, because of:
2^2007 + 3^2008 - 2009 =
= (2^2007-2006) + (3^2008-3) =
= (2^2007-2-2004) + (3^2008-3) =
= 2*(2^2006 - 1 - 1002) + 
+ (3^2008 - 3), where
2^2006 - 1 - 1002 is divided by 3.
    
Therefore, in accordance with above
three criteria, our number in the
condition is divided into 3, 5, 7.
Numbers 3^2008 and 2^2007 in the
decimal notation end in 1 and 8
respectively, thus
2^2007 + 3^2008 - 2009 is divided by 10

2^(2^2007+3^2008-2009) is divided
by 3 * 5 * 7 * 11 = 1155.

Challenge(Math)