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Arithmetic sequence

Source: Mathematics and Youth Magazine (vietnam)

September 16, 2020
number theoryarithmetic sequence

Problem Statement

The sequence (an)\left(a_n \right) is defined by a1=1, a2=2a_1=1, \ a_2=2 and an+2=2an+1−pan, ∀n≥1,a_{n+2} = 2a_{n+1}-pa_n, \ \forall n \ge 1, for some prime p.p. Find all pp for which there exists mm such that am=−3.a_m=-3.
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