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a divides b + c, b divides a + c , c divides a + b

Source: 2020 Dürer Math Competition Finals Day2 E+6 https://artofproblemsolving.com/community/c1622639_2020_

January 7, 2022
number theorydivides

Problem Statement

Positive integers a,ba, b and cc are all less than 20202020. We know that aa divides b+cb + c, bb divides a+ca + c and cc divides a+ba + b. How many such ordered triples (a,b,c)(a, b, c) are there?
Note: In an ordered triple, the order of the numbers matters, so the ordered triple (0,1,2)(0, 1, 2) is not the same as the ordered triple (2,0,1)(2, 0, 1).
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