A student of mine has asked me to solve the following Diophantine equation, but it has been a long time since I looked at these problems. Here is the problem:
Problem: Find the natural number solutions of the equation $$a+b+c+d+e = 2020.$$
Any help is appreciated.
Should be $2019\choose 4$, using stars and bars.
Intuitively, there are $2019$ places to put $4$ bars, thus partitioning the $2020$ stars into $5$ nonempty sets.