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p <=19 divides a_n = 2 x 10^{n + 1} + 19

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 3.5

September 21, 2021
number theorydivides

Problem Statement

We have an a sequence such that an=2⋅10n+1+19a_n = 2 \cdot 10^{n + 1} + 19. Determine all the primes pp, with p≤19p \le 19, for which there exists some n≥1n \ge 1 such that pp divides ana_n.
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