Question 2: Prove that for any 4 integers we can nd 2 integers (say a,b) among the 4 integers such that (1% ab3 is divisible by 14. Hint: start by showing that (1% ab3 is divisible by 2 for any pair of integers selected from the 4, by considering all the cases, i.e., a is even, b is odd, etc. Then use the pigeonhole principle to Show that among the 4 integers there must be 2 that make this expression divisible by 7