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2014 MMATHS Tiebreaker p2 - a_n = n if a_{2n} = a_n + n

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October 8, 2023
MMATHSalgebra

Problem Statement

Let (an)n=1∞(a_n)^{\infty}_{n =1} be a sequence of positive integers with a1<a2<a3<...a_1 < a_2 < a_3 < ... , and for n = 1, 2, 3,..., a2n=an+n.a_{2n} = a_n + n. Furthermore, whenever nn is prime, so is ana_n. Prove that an=na_n = n.
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