Subset

How many subsets with three elements can be formed from the set \(\{1,2,3,\cdots,20\}\)uch that \(4\) is a factor of the product of the three numbers in the subset?

Prime

Let \(x\) be an integer of the form $$x=\underbrace{111\cdots 11}_{n\thinspace times}$$ Show that, if \(x\) is prime then \(n\) is prime.