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sequence k+a_n contains only finitely many primes

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1997 p4

February 20, 2020
Sequenceprimesnumber theory

Problem Statement

Show that there exists an increasing sequence a1,a2,a3,...a_1,a_2,a_3,... of natural numbers such that, for any integer k≥2k \ge 2, the sequence k+ank+a_n (n∈Nn \in N) contains only finitely many primes.
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