MathDB

2

Part of 2020 May Olympiad

Problems(2)

$a+b+c=2020$

Source: May Olympiad 2020 L2 P2

11/27/2020
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.
number theory
Pablo's list

Source: May Olympiad 2020 L1 P2

3/14/2021
Paul wrote the list of all four-digit numbers such that the hundreds digit is 55 and the tens digit is 77. For example, 15731573 and 75707570 are on Paul's list, but 27542754 and 571571 are not. Find the sum of all the numbers on Pablo's list. NoteNote. The numbers on Pablo's list cannot start with zero.
number theory