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
Topic
Number Theory
Difficulty Level
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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