Elementary Diophantine Equation in 5 variables

Question

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.

You may find the Restricted part size or number of parts section of Wikipedia's "Partition (number theory)" article interesting & useful, as it deals specifically with what you're asking about. — John Omielan, Aug 06 '19 at 01:17

score 0 · Answer 1 · answered Aug 06 '19 at 01:33

0

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.

answered Aug 06 '19 at 01:33

Elementary Diophantine Equation in 5 variables

1 Answers1