4. There are 51 software students taking MATH 211. Let p,Pz, .. Psi be their final exam scores. Hence, each p, is an integer and 1< P < 100 for every i. Show that there exists i and j with i j such that p, divides p;. 4b. Show that there exists i and j wi h í < j such that the consecutive sum p, + p+1+ +P; is divisible by 37. 4c. Suppose that P Pa Psi are all distinct and 1 < P < 86 for every i. Show that there exists i and j such that p,- p, - 16.

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