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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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Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.

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