MathDB
$a+b+c=2020$

Source: May Olympiad 2020 L2 P2

November 27, 2020
number theory

Problem Statement

a) Determine if there are positive integers a,ba, b and cc, not necessarily distinct, such that a+b+c=2020a+b+c=2020 and 2a+2b+2c2^a+2^b+2^c it's a perfect square. b) Determine if there are positive integers a,ba, b and cc, not necessarily distinct, such that a+b+c=2020a+b+c=2020 and 3a+3b+3c3^a+3^b+3^c it's a perfect square.
Back to ProblemsView on AoPS