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Show that there exists i and j with i + j such that p, divides p;. а. b. Show that there exists i and j with i < j such that the consecutive sum p; +p;+1++P; is divisible by 37.

Show that there exists i and j with i + j such that p, divides p;. а. b. Show that there exists i and j with i < j such that the consecutive sum p; +p;+1++P; is divisible by 37.

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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Discreet Mathamtics

There are 51 software students taking MATH 211. Let p1, P2, ..., Ps1 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;. а. b. Show that there exists i and j with i< j such that the consecutive sum p;+Pi+1+.+Pj is divisible by 37. Suppose that pi, P2, ..., P51 are all distinct and 1 < pi < 86 for every i. Show that с. there exists i and j such that pi – Pj = 16.
Transcribed Image Text:There are 51 software students taking MATH 211. Let p1, P2, ..., Ps1 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;. а. b. Show that there exists i and j with i< j such that the consecutive sum p;+Pi+1+.+Pj is divisible by 37. Suppose that pi, P2, ..., P51 are all distinct and 1 < pi < 86 for every i. Show that с. there exists i and j such that pi – Pj = 16.
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