MathDB
Good sets

Source: Romanian District Olympiad 2014, Grade 6, P2

June 15, 2014
combinatorics proposedcombinatorics

Problem Statement

We call a nonempty set MM good if its elements are positive integers, each having exactly 44 divisors. If the good set MM has nn elements, we denote by SMS_{M} the sum of all 4n4n divisors of its members (the sum may contain repeating terms).
a) Prove that A={2⋅37,19⋅37,29⋅37}A=\{2\cdot37,19\cdot37,29\cdot37\} is good and SA=2014S_{A}=2014.
b) Prove that if the set BB is good and 8∈B8\in B, then SB≠2014S_{B}\neq2014.
Back to ProblemsView on AoPS