MathDB
f_k(x)f_{k+1}(x) = f_{k+1}(f_{k+2}(x))

Source: Indian Postal Coaching 2009 set 6 p3

May 26, 2020
polynomialalgebra

Problem Statement

Let n≥3n \ge 3 be a positive integer. Find all nonconstant real polynomials f1(x),f2(x),...,fn(x)f_1(x), f_2(x), ..., f_n(x) such that fk(x)fk+1(x)=fk+1(fk+2(x))f_k(x)f_{k+1}(x) = f_{k+1}(f_{k+2}(x)), 1≤k≤n1 \le k \le n for all real x. [All suffixes are taken modulo nn.]
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