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[n p/q], [cn + d],

Source: Czech and Slovak Olympiad 1989, National Round, Problem 3

September 13, 2024
number theory

Problem Statement

For given coprime numbers p>q>0p > q > 0, find all pairs of real numbers c,dc,d such that for the sets A={[npq],n∈N}  and  B={[cn+d],n∈N}A = \left\{ \left[n\frac{p}{q}\right] , n \in N \right\} \ \ and \ \ B = \{[cn + d], n \in N\} where A∩B=∅A \cap B = \emptyset, A∪B=NA \cup B = N, where N={1,2,3,...}N = \{1, 2, 3, ...\} is the set of all natural numbers.
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