MathDB

1

Part of 2021 Argentina National Olympiad

Problems(3)

Argentina MO 2021 National Level 1 P1

Source:

4/23/2022
Determine all pairs of prime numbers pp and qq greater than 11 and less than 100100, such that the following five numbers: p+6,p+10,q+4,q+10,p+q+1,p+6,p+10,q+4,q+10,p+q+1, are all prime numbers.
contestsnumber theoryprime numbers
Argentina MO 2021 National Level 2 P1

Source:

4/23/2022
You have two blackboards AA and BB. You have to write on them some of the integers greater than or equal to 22 and less than or equal to 2020 in such a way that each number on blackboard AA is co-prime with each number on blackboard B.B. Determine the maximum possible value of multiplying the number of numbers written in AA by the number of numbers written in BB.
contestscoprime numbersnumber theory
Argentina MO 2021 National Level 3 P1

Source:

4/24/2022
An infinite sequence of digits 11 and 22 is determined by the following two properties:
i) The sequence is built by writing, in some order, blocks 1212 and blocks 112.112. ii) If each block 1212 is replaced by 11 and each block 112112 by 22, the same sequence is again obtained.
In which position is the hundredth digit 11? What is the thousandth digit of the sequence?
SequencecombinatoricscontestsArgentina