MathDB

Let

\mathcal{F}

be the set of polynomials

f(x)

with integer coefficients for which there exists an integer root of the equation

f(x)=1

. For all

k>1

, let

m_k

be the smallest integer greater than one for which there exists

f(x)\in \mathcal{F}

such that

f(x)=m_k

has exactly

k

distinct integer roots. If the value of

\sqrt{m_{2021}-m_{2020}}

can be written as

m\sqrt{n}

for positive integers

m,n

where

n

is squarefree, compute the largest integer value of

k

such that

2^k

divides

\frac{m}{n}

Problem Statement