MathDB

We say that a quadrilateral

Q

is tangential if a circle can be inscribed into it, i.e. there exists a circle

C

that does not meet the vertices of

Q

, such that it meets each edge at exactly one point. Let

N

be the number of ways to choose four distinct integers out of

\{1, . . . , 24\}

so that they form the side lengths of a tangential quadrilateral. Find the largest prime factor of

N

Problem Statement