# Thread: a problem with generating functions

1. ## a problem with generating functions

Hey, I need a little help

The problem is: Using generating functions (https://en.wikipedia.org/wiki/Generating_function) find out how many solutions the equation has
if

and

Thanks

2. ## Re: a problem with generating functions

Originally Posted by Breh
has
if

and

$\left( {\sum\limits_{k = 0}^9 {{x^k}} } \right)\left( {\sum\limits_{k = 5}^{14} {{x^k}} } \right)\left( {\sum\limits_{k = 10}^{19} {{x^k}} } \right){\left( {\sum\limits_{k = 0}^{25} {{x^k}} } \right)^3}$

SEE HERE

Thank you!

4. ## Re: a problem with generating functions

I am sorry but can you give me a short explanation why the last sum is from k=0 to 25? And why the exponent is three?

5. ## Re: a problem with generating functions

Originally Posted by Breh
I am sorry but can you give me a short explanation why the last sum is from k=0 to 25? And why the exponent is three?
The answer is simple $10+5+25=40$. We have two with restricted minimums of $10~\&~5$ so all other cannot add to more that $25$.