MathDB

N1

Part of 2020 Romanian Master of Mathematics Shortlist

Problems(1)

Number Theory FE

Source: 2020 RMM Shortlist N1

10/8/2022
Determine all pairs of positive integers (m,n)(m, n) for which there exists a bijective function f:Zm×Zn→Zm×Znf : \mathbb{Z}_m \times \mathbb{Z}_n \to \mathbb{Z}_m \times \mathbb{Z}_nsuch that the vectors f(v)+vf(\mathbf{v}) + \mathbf{v}, as v\mathbf{v} runs through all of Zm×Zn\mathbb{Z}_m \times \mathbb{Z}_n, are pairwise distinct.
(For any integers aa and bb, the vectors [a,b],[a+m,b][a, b], [a + m, b] and [a,b+n][a, b + n] are treated as equal.)
Poland, Wojciech Nadara
number theoryfunctionRMMRMM 2020RMM Shortlist