- Andrei Frimu, Yimin Ge, Ofir Gorodetsky, Daniel Kohen, David Kotik, Hojoo Lee, Soo-Hong Lee, Cosmin Pohoata, Ho Chung Siu, Peter Vandendriessche, Problems in Elementary Number Theory 1 (Fall 2008) (39 pages; link to the PDF file).
In this volume, you will meet the solutions of the problems from the first season of PEN biweek project. Additional details about this project can be read from http://projectpen.wordpress.com/.
- Hojoo Lee, Tom Lovering, Cosmin Pohoata, INFINITY, 2008. (204 pages; both TeX and PDF are available for download)
In this never-ending project, which bears the name Infinity, we offer a delightful playground for young mathematicians and try to continue the beautiful spirit of IMO and MathLinks. Infinity begins with a chapter on elementary number theory and mainly covers Euclidean geometry and inequalities. We re-visit beautiful well-known theorems and present heuristics for elegant problem-solving. Our aim in this weblication is not just to deliver must-know techniques in problem-solving. Young readers should keep in mind that our aim in this project is to present the beautiful aspects of Mathematics. Eventually, Infinity will admit bridges between Olympiads Mathematics and undergraduate Mathematics.
Additional information related to this project can be found on Hojoo Lee’s blog at: http://ideahitme.wordpress.com/infinity/.
- Cosmin Pohoata, A combinatorial proof of Lindstr”om’s theorem on unions of subsets of a finite set. (Link to the PDF file)
In this note, we give a combinatorial proof of Bernt Lindstr\”om’s theorem that if A_{1}, A_{2},…, A_{n+1} are nonempty subsets of an n-element set, then we can find two disjoint and nonempty groups of indices \left\{i_{1},\ i_{2},\ \ldots,\ i_{k}\right\} and \left\{j_{1},\ j_{2},\ \ldots,\ j_{m}\right\} such that
A_{i_{1}} \cup A_{i_{2}} \cup \ldots \cup A_{i_{k}} = A_{j_{1}} \cup A_{j_{2}} \cup \ldots \cup A_{j_{m}}.
