(a) How many positive factors are there of 2009?
There are 6 positive factors: .
(b) How many solutions in positive integers are there to the equation: .
Place 2009 objects in a row, leaving one space between them.
. . . . .
Select two of the 2008 spaces and insert "dividers".
. . So that:.
There are: . possible partitions.
Therefore, there are 2,015,028 solutions to
(c) How many solutions in positive integers x,y,z are there to the equation: .
The prime factorization 2009 is: .
There are 15 solutions to