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NT sequence

Source: Cplp Problem 6

July 15, 2017
number theorySequencesDivisibility

Problem Statement

Let (an)(a_n) be defined by:
a1=2,an+1=an3−an+1 a_1 = 2, \qquad a_{n+1} = a_n^3 - a_n + 1
Consider positive integers n,pn,p, where pp is an odd prime. Prove that if p∣anp | a_n, then p>np > n.
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