MathDB
many days of the year can be Adel’s birthday?

Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E6

May 25, 2024
number theory

Problem Statement

In Eldorado a year has 2020 months, and each month has 2020 days. One day Brigi asked Adél who lives in Eldorado what day her birthday is. Adél answered that she is only going to tell her the product of the month and the day in her birthday. (For example, if she was born on the 1919th day of the 44th month, she would say 419=764 \cdot 19 = 76.) From this, Brigi was able to tell Adél’s birthday. Based on this information, how many days of the year can be Adél’s birthday?