Construct a polynomial $f$ over $\mathbb{Q}$ such that the galois group of the splitting field of $f$ is the monster group
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5$ for an open problem? More seriously, it doesn't make a lot of sense to ask for an explicit polynomial. Check this for more info. https://www.quora.com/What-is-known-about-the-polynomial-of-which-the-Monster-group-is-the-Galois-group
@ Alessandro: That's exactly what I was also thinking.
This website isn't here for people to post trivial homework questions ◔_◔
@Alessandro Iraci yes but I want an explicit polynomial