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MMO 299 Moscow MO 1955 increasing arithmetic progression of primes

Source:

August 17, 2019
number theoryArithmetic ProgressionSequenceprimesdivisible

Problem Statement

Suppose that primes a1,a2,...,apa_1, a_2, . . . , a_p form an increasing arithmetic progression and a1>pa_1 > p. Prove that if pp is a prime, then the difference of the progression is divisible by pp.
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