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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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    This can be solved via [Stars and Bars](https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)). – lulu Aug 06 '19 at 01:15
  • You may find the [Restricted part size or number of parts](https://en.wikipedia.org/wiki/Partition_(number_theory)#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
  • arithmetic mean is 404 –  Aug 06 '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.