MathDB

f(x)q(x)-p(x) of form \sum\limits_{2n<k\leq 3n} (a^k + x^k) have same p(x)/q(x)

Source: 1973 Swedish Mathematical Competition p5

March 26, 2021

algebrapolynomial

Problem Statement

f(x)

is a polynomial of degree

2n

. Show that all polynomials

p(x)

q(x)

of degree at most

n

such that

f(x)q(x)-p(x)

has the form

\sum\limits_{2n<k\leq 3n} (a^k + x^k)

have the same

p(x)/q(x)