MathDB

Problem 1

Part of 2008 VJIMC

Problems(2)

FE over Z, 19f(x)-17f(f(x))=2x

Source: VJIMC 2008 2.1

6/17/2021
Find all functions f:Z→Zf:\mathbb Z\to\mathbb Z such that 19f(x)−17f(f(x))=2x19f(x)-17f(f(x))=2xfor all x∈Zx\in\mathbb Z.
fefunctional equationalgebra
complex roots of polynomial

Source: VJIMC 2008 1.1

6/16/2021
Find all complex roots (with multiplicities) of the polynomial p(x)=∑n=12008(1004−∣1004−n∣)xn.p(x)=\sum_{n=1}^{2008}(1004-|1004-n|)x^n.
complex numbersPolynomialsalgebrapolynomial