MathDB

2

Part of 2013 Czech-Polish-Slovak Junior Match

Problems(2)

coloring all postitive integers red or green

Source: Czech-Polish-Slovak Junior Match 2013, Individual p2 CPSJ

3/14/2020
Each positive integer should be colored red or green in such a way that the following two conditions are met: - Let nn be any red number. The sum of any nn (not necessarily different) red numbers is red. - Let mm be any green number. The sum of any mm (not necessarily different) green numbers is green. Determine all such colorings.
ColoringcombinatoricsSum
sum of the three largest divisors of n is 1457

Source: Czech-Polish-Slovak Junior Match 2013, Team p2 CPSJ

3/21/2020
Find all natural numbers nn such that the sum of the three largest divisors of nn is 14571457.
number theorysum of divisors