MathDB
set decomposition

Source: miklos schweitzer 1993 q2

October 21, 2021
number theory

Problem Statement

Let A be a subset of natural numbers and let k , r be positive integers. Suppose that for any r different elements selected from A , their greatest common divisor has at most k different prime factors. Prove that A can be partitioned into B and C , where any element of B has at most k + 1 different prime divisors and ∑n∈C1n<∞\sum_{n\in C} \frac{1}{n} <\infty
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