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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. There are 51 software students taking MATH 211. Let pi,Pa, .. Ps1 be their final exam scores. Hence, each p, is an integer and 1< Pi< 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 wih i < j such that the consecutive sum p, + pi+1t +pj is divisible by 37. 4c. Suppose that P. Pa Pst are all distinct and 1 < P < 86 for every i. Show that there exists i and j such that p P-P,-16.
Transcribed Image Text:4. There are 51 software students taking MATH 211. Let pi,Pa, .. Ps1 be their final exam scores. Hence, each p, is an integer and 1< Pi< 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 wih i < j such that the consecutive sum p, + pi+1t +pj is divisible by 37. 4c. Suppose that P. Pa Pst are all distinct and 1 < P < 86 for every i. Show that there exists i and j such that p P-P,-16.
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