MathDB
Interesting problem

Source: Iranian Third Round 2020 Algebra exam Problem4

November 20, 2020
polynomialequationalgebra

Problem Statement

We call a polynomial P(x)P(x) intresting if there are 13981398 distinct positive integers n1,...,n1398n_1,...,n_{1398} such that P(x)=∑xni+1P(x)=\sum_{}{x^{n_i}}+1 Does there exist infinitly many polynomials P1(x),P2(x),...P_1(x),P_2(x),... such that for each distinct i,ji,j the polynomial Pi(x)Pj(x)P_i(x)P_j(x) is interesting.
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