MathDB

4

Part of 2015 Cuba MO

Problems(2)

A, B subests of 1-100, n \in A => 2n + 2 \in B

Source: 2015 Cuba 1.4

9/20/2024
Let AA and BB be two subsets of {1,2,3,4,...,100}\{1, 2, 3, 4, ..., 100\}, such that ∣A∣=∣B∣|A| = |B| and A∩B=∅A\cap B =\emptyset. If n∈An \in A implies that 2n+2∈B2n + 2 \in B, determine the largest possible value of ∣A∪B∣ |A \cup B|.
number theory
4-digit numbers

Source: 2015 Cuba 2.4

9/20/2024
Let A=abcd‾A = \overline{abcd} be a 44-digit positive integer, such that a≥7a\ge 7 and a>b>c>d>0a > b >c > d > 0. Let us consider a positive integer B=dcba‾B = \overline{dcba}. If all digits of A+BA+B are odd, determine all possible values of AA.
number theoryDigits