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greatest element from S

Source: VietNam TST 2004, problem 6

May 9, 2004
number theory solvednumber theory

Problem Statement

Let SS be the set of positive integers in which the greatest and smallest elements are relatively prime. For natural nn, let SnS_n denote the set of natural numbers which can be represented as sum of at most nn elements (not necessarily different) from SS. Let aa be greatest element from SS. Prove that there are positive integer kk and integers bb such that ∣Sn∣=a⋅n+b|S_n| = a \cdot n + b for all n>k n > k .
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