How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?

# Parity in Mathematics | Is the Sum Zero?

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 $d_1 + d_2 + ... + d_{2019}$.

First, 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?

Now, watch this video

Next

Try another problem