MathDB
Gcd sequence

Source: MEMO 2023 T8

August 25, 2023
number theory

Problem Statement

Let A,B∈NA, B \in \mathbb{N}. Consider a sequence x1,x2,…x_1, x_2, \ldots such that for all n≥2n\geq 2, xn+1=A⋅gcd⁡(xn,xn−1)+B.x_{n+1}=A \cdot \gcd(x_n, x_{n-1})+B. Show that the sequence attains only finitely many distinct values.
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