Problems(2)
2022 naturals in a row, product of 2 is a perfect cube
Source: 2022 South Russian Girls MO - Assara Juniors p2
2/28/2024
There are natural numbers written in a row. Product of any two adjacent numbers is a perfect cube. Prove that the product of the two extremes is also a perfect cube.
number theoryperfect cube
100 numbers in a circle, min number of good pairs
Source: 2022 South Russian Girls MO - Assara Seniors p2
3/1/2024
Numbers are arranged in a circle in some order. A good pair is a pair of numbers of the same parity, between which there are exactly numbers. What is the smallest possible number good pairs?
combinatorics