MathDB

Suppose that

P(x)

is a monic cubic polynomial with integer roots, and suppose that

\frac{P(a)}{a}

is an integer for exactly

6

integer values of

a

. Suppose furthermore that exactly one of the distinct numbers

\frac{P(1) + P(-1)}{2}

and

\frac{P(1) - P(-1)}{2}

is a perfect square. Given that

P(0) > 0

, find the second-smallest possible value of

P(0).

Proposed by Andrew Wu

Problem Statement