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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.

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    $\begingroup$ This can be solved via Stars and Bars. $\endgroup$ – lulu Aug 6 '19 at 1:15
  • $\begingroup$ 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. $\endgroup$ – John Omielan Aug 6 '19 at 1:17
  • $\begingroup$ arithmetic mean is 404 $\endgroup$ – user645636 Aug 6 '19 at 11:22
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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.

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