Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 711. (December 2017)

A. 711. For which pairs \(\displaystyle (m,n)\) does there exist an injective function \(\displaystyle f\colon \mathbb{R}^2\to\mathbb{R}^2\) under which the image of every regular \(\displaystyle m\)-gon is a regular \(\displaystyle n\)-gon. (Note that \(\displaystyle m,n\ge 3\), and that by a regular \(\displaystyle N\)-gon we mean the union of the boundary segments, not the closed polygonal region.)

Proposed by: Sutanay Bhattacharya, Bishnupur, India

(5 pont)

Deadline expired on January 10, 2018.


6 students sent a solution.
5 points:Gáspár Attila, Imolay András, Matolcsi Dávid.
4 points:Schrettner Jakab.
3 points:2 students.

Problems in Mathematics of KöMaL, December 2017