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the term $x_n$ is the greatest odd integer of $x_{n-1}+x_{n-2}$

Source: Moldova TST 1997

August 8, 2023
number theory

Problem Statement

Let aa and bb be two odd positive integers. Define the sequence (xn)n∈N(x_n)_{n\in\mathbb{N}} as such: x1=a,x2=b,x_1=a, x_2=b, for every n≥3n\geq3 the term xnx_n{} is the greatest odd integer of xn−1+xn−2x_{n-1}+x_{n-2}. Show that starting with a term, all the following terms are constant.
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