Problem B. 4698. (March 2015)

B. 4698. Give an example for sets \(\displaystyle H_1,H_2,\ldots\subset\mathbb{N}\) for which the following conditions hold:

\(\displaystyle a)\) \(\displaystyle |H_n|=n\) for all positive integers \(\displaystyle n\).

\(\displaystyle b)\) For all positive integers \(\displaystyle n\) and \(\displaystyle k\), \(\displaystyle H_n \cap H_k = H_{(n,k)}\), where \(\displaystyle (n,k)\) is the greatest common divisor of \(\displaystyle n\) and \(\displaystyle k\).

(5 pont)

Deadline expired on April 10, 2015.

Statistics:

47 students sent a solution.
5 points:	Baran Zsuzsanna, Bindics Boldizsár, Döbröntei Dávid Bence, Gáspár Attila, Glasznova Maja, Kerekes Anna, Kovács 246 Benedek, Lajkó Kálmán, Molnár-Sáska Zoltán, Nagy-György Pál, Porupsánszki István, Sal Kristóf, Schwarcz Tamás, Szebellédi Márton, Szécsényi Nándor, Tóth Viktor, Varga-Umbrich Eszter, Williams Kada, Zsakó Ágnes.
4 points:	Andó Angelika, Árvai Balázs, Csépai András, Imolay András, Katona Dániel, Keresztfalvi Bálint, Mócsy Miklós, Nagy Dávid Paszkál, Nagy Kartal, Wei Cong Wu, Záhorský Ákos.
3 points:	4 students.
2 points:	6 students.
1 point:	2 students.
0 point:	3 students.
Unfair, not evaluated:	2 solutionss.

Problems in Mathematics of KöMaL, March 2015