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a_1 = a_3 when a_i+1=p(a_1), integer polynomila p(x)

Source: Austrian - Polish 1990 APMC

May 7, 2020
algebrapolynomialInteger Polynomial

Problem Statement

p(x)p(x) is a polynomial with integer coefficients. The sequence of integers a1,a2,...,ana_1, a_2, ... , a_n (where n>2n > 2) satisfies a2=p(a1),a3=p(a2),...,an=p(an−1),a1=p(an)a_2 = p(a_1), a_3 = p(a_2), ... , a_n = p(a_{n-1}), a_1 = p(a_n). Show that a1=a3a_1 = a_3.
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