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Combinatorial number theory

Source: Czech and Slovak Olympiad 1981, National Round, Problem 4

October 11, 2024
number theorycombinatoricsprime numbersSequence

Problem Statement

Let nn be a positive integer. Show that there is a prime pp and a sequence (ak)k≥1\left(a_k\right)_{k\ge1} of positive integers such that the sequence (p+nak)k≥1\left(p+na_k\right)_{k\ge1} consists of distinct primes.
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