MathDB

1

Part of 2006 May Olympiad

Problems(2)

(a+1)/b and (b+1)/a are naturals

Source: XII May Olympiad (Olimpiada de Mayo) 2006 L2 P1

9/19/2022
Determine all pairs of natural numbers aa and bb such that a+1b\frac{a+1}{b} and b+1a\frac{b+1}{a} they are natural numbers.
number theorydivides
digits callendar date reflected at a mirror

Source: XII May Olympiad (Olimpiada de Mayo) 2006 L1 P1

9/22/2022
A digital calendar displays the date: day, month, and year, with 22 digits for the day, 22 digits for the month, and 22 digits for the year. For example, 01−01−0101-01-01 is January 11, 20012001 and 05−25−2305-25-23 is May 2525, 20232023. In front of the calendar is a mirror. The digits of the calendar are as in the figure https://cdn.artofproblemsolving.com/attachments/c/5/a08a4e34071fff4d33b95b23690254f55b33e1.gif
If 0,1,2,50, 1, 2, 5, and 88 are reflected, respectively, in 0,1,5,20, 1, 5, 2, and 88, and the other digits lose meaning when reflected, determine how many days of the century, when reflected in the mirror, also correspond to a date.
combinatorics