Let n be a positive integer and Sn be the set of all positive integers not exceeding n and relatively prime to n. Let f(n) be the smallest positive integer for which the set Sn can be partitioned into f(n) disjoint subsets, such that each of these subsets is an arithmetic progression. Show that there are infinitely many pairs (a, b) such that a, b > 2025, a|b and f(a) 6 |f(b).
Correct Solutions by,
- Toshihiro Shimizu Kawasaki, Japan
- Mahmut Semih Baş İstanbul Technical University
- Ramazan Karaşahin Ankara
- Hasan Zübeyr Demir Ankara
- Magnus Jakobsson Lund, Sweden
- Özgür Soysal Bilkent University
- Murat Beşli Politecnico di Torino, Italy
- Arda Karahan Trabzon Fen Lisesi
- Ananda Raidu Rajahmundry, India
- Serhat Güldoğan Koç University
Solution 2505c.pdf (bilkent.edu.tr)