☝️ Integer Equations

Partitioning problem++

Determine the number of non-negative integer solutions to an equation.

Theory:

The number of non-negative integer solutions to the equation:

$$a_1+a_2+\cdots +a_k=n$$

is given by:

$$C(n+k-1,k-1)=\frac{(n+k-1)!}{(k-1)!n!}$$

Where:

• $n$ : Total sum
• $k$ : Number of variables