MathDB

3

Part of 2019 South East Mathematical Olympiad

Problems(2)

Infinitely many k such that f(k)=1

Source: CSMO 2019 Grade 10 Problem 3

7/30/2019
Let f:N→Nf:\mathbb{N}\rightarrow \mathbb{N} be a function such that f(ab)f(ab) divides max⁡{f(a),b}\max \{f(a),b\} for any positive integers a,ba,b. Must there exist infinitely many positive integers kk such that f(k)=1f(k)=1?
functionnumber theory
Cut the perfect square out

Source: CSMO 2019 Grade 11 Problem 3

7/30/2019
nn symbols line up in a row, numbered as 1,2,...,n1,2,...,n from left to right. Delete every symbol with squared numbers. Renumber the rest from left to right. Repeat the process until all nn symbols are deleted. Let f(n)f(n) be the initial number of the last symbol deleted. Find f(n)f(n) in terms of nn and find f(2019)f(2019).
combinatorics