Hello, aab300!

(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: .

We have:

. .

There are 15 solutions to