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# Understand the problem

For each $$n \in \mathbb{N}$$ let $$d_n$$ denote the G.C.D. of n and (2019 – n). Find the value of $$d_1 + d_2 + … + d_{2019}$$.

##### Source of the problem
Regional Math Olympiad, 2019, Maharashtra, Goa Region Problem 1
Number Theory
5/10

##### Suggested Book
Challenges and Thrills in Pre College Mathematics

# But first, can you try these problems?

1. Show that G.C.D. of k and 0 is k for any positive integer k.
2. Show rigorously that G.C.D. (a, b) = G.C.D. (a, a+b) for any non-negative integers a and b
3. Can you find and prove a similar result with a negative sign?

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