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Argentina MO 2021 National Level 3 P5

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April 24, 2022
number theoryprime numberscontestsArgentina

Problem Statement

The sequence an(n≥1)a_n (n\geq 1) of natural numbers is defined as an+1=an+bn,a_{n+1}=a_n+b_n, where bnb_n is the number that has the same digits as ana_n but in the opposite order (bnb_n can start with 00). For example, if a1=180,a_1=180, then a2=261,a3=423.a_2=261, a_3=423.
a) Decide if a1a_1 can be chosen so that a7a_7 is prime. b) Decide if a1a_1 can be chosen so that a5a_5 is prime.
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