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Source: 2022 AIME II Problem 13

February 17, 2022
algebrapolynomialAMCAIMEAIME II

Problem Statement

There is a polynomial P(x)P(x) with integer coefficients such that P(x)=(x2310−1)6(x105−1)(x70−1)(x42−1)(x30−1)P(x)=\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)} holds for every 0<x<1.0<x<1. Find the coefficient of x2022x^{2022} in P(x)P(x)
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