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a_n=P(a_{n-1})

Source: 2022 Thailand MO Day 2 P7

June 15, 2022
number theorySequence

Problem Statement

Let d≥2d \geq 2 be a positive integer. Define the sequence a1,a2,…a_1,a_2,\dots by a1=1 and an+1=and+1 for all n≥1.a_1=1 \ \text{and} \ a_{n+1}=a_n^d+1 \ \text{for all }n\geq 1. Determine all pairs of positive integers (p,q)(p, q) such that apa_p divides aqa_q.
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