MathDB
ISI 2019 : Problem #7

Source: I.S.I. 2019

May 5, 2019
isiIndian Statistical Institute2019polynomialInteger Polynomialalgebra

Problem Statement

Let ff be a polynomial with integer coefficients. Define a1=f(0) , a2=f(a1)=f(f(0)) ,a_1 = f(0)~,~a_2 = f(a_1) = f(f(0))~, and  an=f(an−1)~a_n = f(a_{n-1}) for n⩾3n \geqslant 3.
If there exists a natural number k⩾3k \geqslant 3 such that ak=0a_k = 0, then prove that either a1=0a_1=0 or a2=0a_2=0.
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