MathDB

Putnam 1940 A6

Source: Putnam 1940

February 22, 2022

Putnamalgebrapolynomial

Problem Statement

Let

f(x)

be a polynomial of degree

n

such that

f(x)^{p}

is divisible by

f'(x)^{q}

for some positive integers

p,q

. Prove that

f(x)

is divisible by

f'(x)

and that

f(x)

has a single root of multiplicity

n

.

Back to Problems View on AoPS