MathDB
Bijection from Z to dZ

Source: Romanian TST Problem 4 Day 2

May 25, 2020
number theorygreatest common divisorbezout s identitynumber theory unsolved

Problem Statement

Let DD be a non-empty subset of positive integers and let dd be the greatest common divisor of DD, and let dZ=[dn:n∈Z]d\mathbb{Z}=[dn: n \in \mathbb{Z} ]. Prove that there exists a bijection f:Z→dZf: \mathbb{Z} \rightarrow d\mathbb{Z} such that ∣f(n+1)−f(n)∣| f(n+1)-f(n)| is member of DD for every integer nn.
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