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Square-free numbers with certain gap

Source: 2020 China Southeast 11.7

August 7, 2020
number theory

Problem Statement

Arrange all square-free positive integers in ascending order a1,a2,a3,…,an,…a_1,a_2,a_3,\ldots,a_n,\ldots. Prove that there are infinitely many positive integers nn, such that an+1−an=2020a_{n+1}-a_n=2020.
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