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Algebra with primes

Source: Serbian national olympiad 2022 P6

April 8, 2022
algebraprimesSerbian competition

Problem Statement

Let pp and qq be different primes, and α∈(0,3)\alpha\in (0, 3) a real number. Prove that in sequence [α],[2α],[3α]…\left[ \alpha \right] , \left[ 2\alpha \right] , \left[ 3\alpha \right] \dots exists number less than 2pq2pq, divisible by pp or qq.
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