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

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

[/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version="3.25"][et_pb_column type="4_4" _builder_version="3.25" custom_padding="|||" custom_padding__hover="|||"][et_pb_accordion open_toggle_text_color="#0c71c3" _builder_version="4.0" toggle_font="||||||||" body_font="Raleway||||||||" text_orientation="center" custom_margin="10px||10px"][et_pb_accordion_item title="Source of the problem" open="on" _builder_version="4.0"]Regional Math Olympiad, 2019, Maharashtra, Goa Region Problem 1[/et_pb_accordion_item][et_pb_accordion_item title="Topic" _builder_version="4.0" open="off"]Number Theory[/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="4.0" open="off"]5/10

# But first, can you try these problems?

[/et_pb_text][et_pb_text _builder_version="4.0"]
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?

# Similar Problems

[/et_pb_text][et_pb_post_slider include_categories="9" _builder_version="3.22.4"][/et_pb_post_slider][et_pb_divider _builder_version="3.22.4" background_color="#0c71c3"][/et_pb_divider][/et_pb_column][/et_pb_row][/et_pb_section]