6 is too small...

True or False?

"There exists a positive integer $n$ such that the set $[n, n+1, n+2, n+3, n+4, n+5]$ can be partitioned into two subsets so that the product of the numbers in each subset is equal."

Bonus : What if it isn't just $6$ consecutive integers? What about $9$ ? $16$ ? $4n+2$ , if $4n+3$ is a prime/composite?

Taken from IMO.