The Pólya conjecture is a disproven conjecture in number theory. It involves the Liouville function \(\lambda(n)\), defined as +1 if \(n\) has an even number of prime factors and -1 if \(n\) has an odd number of prime factors, counting multiplicity. The conjecture states that for all \(n > 1\) the summatory Liouville function \(L(n) = \sum_{i = 1}^{n} \lambda(i)\) is always non-positive.