MathDB

Number Theory FE

Source: 2020 RMM Shortlist N1

October 8, 2022

number theoryfunctionRMMRMM 2020RMM Shortlist

Problem Statement

Determine all pairs of positive integers

(m, n)

for which there exists a bijective function

f : \mathbb{Z}_m \times \mathbb{Z}_n \to \mathbb{Z}_m \times \mathbb{Z}_n

such that the vectors

f(\mathbf{v}) + \mathbf{v}

, as

\mathbf{v}

runs through all of

\mathbb{Z}_m \times \mathbb{Z}_n

, are pairwise distinct.
(For any integers

a

and

b

, the vectors

[a, b], [a + m, b]

and

[a, b + n]

are treated as equal.)
Poland, Wojciech Nadara

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