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Primes in arithmetic progression

Source: Mathematics Regional Olympiad of Mexico Southeast 2021 P2

October 22, 2021
number theoryprime numbersarithmetic sequence

Problem Statement

Let n≥2021n\geq 2021. Let a1<a2<⋯<ana_1<a_2<\cdots<a_n an arithmetic sequence such that a1>2021a_1>2021 and aia_i is a prime number for all 1≤i≤n1\leq i\leq n. Prove that for all pp prime with p<2021,pp<2021, p divides the diference of the arithmetic sequence.
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