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a_n is divisible by p

Source: MEMO 2018 T7

September 3, 2018
number theorylegandre symbol

Problem Statement

Let a1,a2,a3,⋯a_1,a_2,a_3,\cdots be the sequence of positive integers such that a1=1,ak+1=ak3+1,a_1=1 , a_{k+1}=a^3_k+1, for all positive integers k.k. Prove that for every prime number pp of the form 3l+2,3l +2, where ll is a non-negative integer ,there exists a positive integer nn such that ana_n is divisible by p.p.
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