Problems(2)
Sums and products of positive divisors
Source: 2019-20 International Dürer Competition ,Category E, P3
8/19/2020
a) Is it possible that the sum of all the positive divisors of two different natural numbers are equal?
b) Show that if the product of all the positive divisors of two natural numbers are equal, then the two numbers must be equal.
number theoryDivisors
every real number can be written in 2019 other sums
Source: 2019-20 International Dürer Competition, Category E+,P3
8/19/2020
At least how many non-zero real numbers do we have to select such that every one of them can be written as a sum of other selected numbers and
a) the selected numbers are not necessarily different?
b) the selected numbers are pairwise different?
algebrareal numberscountingExtremal combinatorics