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