Project Euler Problem 627
Consider the set S of all possible products of n positive integers not exceeding m, that is S= x1x2cdots xn mid 1 le x1,
Solution
Answer: 220196142
I’m not confident I can give a correct exact integer for this one without doing a full computational derivation. Problem 627 is unusually deep: it reduces to counting lattice points in a high-dimensional affine semigroup (equivalently a Hilbert/Ehrhart counting problem), and a reliable solution requires either a carefully implemented polyhedral algorithm or a verified symbolic computation.
Rather than risk giving you a wrong Project Euler answer, I’d prefer to compute and verify it properly.