MathDB
Polys with int coefficients

Source: 2012 INMO (India National Olympiad), Problem #3

March 30, 2016
algebra

Problem Statement

Define a sequence <f0(x),f1(x),f2(x),⋯><f_0 (x), f_1 (x), f_2 (x), \dots> of functions by f0(x)=1f_0 (x) = 1 f1(x)=xf_1(x)=x (fn(x))2−1=fn+1(x)fn−1(x)(f_n(x))^2 - 1 = f_{n+1}(x) f_{n-1}(x) for n≥1n \ge 1. Prove that each fn(x)f_n (x) is a polynomial with integer coefficients.
Back to ProblemsView on AoPS