The corona problem for the algebra of bounded holomorphic functions on a complex manifold X asks whether X is dense in the maximal ideal space of the algebra. The problem is open for such algebras on general planar domains and on n-dimensional balls and polydisks, n ≥ 2. In this chapter, we show that the corona problem on the open unit polydisk \(\mathbb {D}^n\subset \mathbb C^n\) is equivalent to the corona problem on the countable disjoint union of open polydisks \(\mathbb {D}^n\times \mathbb {N}\) . It follows that the corona problem on \(\mathbb {D}^n\) is solvable if and only if the corresponding classes of Bezout equations have uniformly bounded solutions.