Problem 2, as you have it written, is incorrect. For example, for n=2, ,
and for n=4,
neither of which is divisible by 80.
Now, if you consider odd n greater that 1...
When n = 2k -1 for some integer, can be written as . The last three factors are even and 4 divides either 2k or 2k-2. So 16 divides the product. If 5 does not divide any among 2k-1 and 2k-2 and 2k, then it must leave remainder 2 or 3 when it divides n. The second factor is . If n=5m+2 or 5m+3, then is and respectively.