There are 51 software students taking MATH 211. Let p1, P2,..., Ps1 be their final cam 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;. OShow that there exists i and j with i
There are 51 software students taking MATH 211. Let p1, P2,..., Ps1 be their final cam 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;. OShow that there exists i and j with i
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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![4c.
Suppose that pi, P2, ..., P51 are all distinct and 1 < Pi < 86 for every i. Show that
there exists i and j such that pi – Pj - 16.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc12a3358-77cb-4e4c-8e25-68008f46381b%2F2a5242a3-37b7-4fad-bbbf-873b4c72d249%2Fz37gbf_processed.png&w=3840&q=75)
Transcribed Image Text:4c.
Suppose that pi, P2, ..., P51 are all distinct and 1 < Pi < 86 for every i. Show that
there exists i and j such that pi – Pj - 16.
![4
There are 51 software students taking MATH 211. Let p1, P2, ..., P51 be their final
exam scores. Hence, each p; is an integer and 1 < p; < 100 for every i.
4a.
Show that there exists i and j with i + j such that p; divides p;.
4b.
Show that there exists i and j with i < j such that the consecutive sum p;+Pi+1+…+Pj
is divisible by 37.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc12a3358-77cb-4e4c-8e25-68008f46381b%2F2a5242a3-37b7-4fad-bbbf-873b4c72d249%2Facailnn_processed.png&w=3840&q=75)
Transcribed Image Text:4
There are 51 software students taking MATH 211. Let p1, P2, ..., P51 be their final
exam scores. Hence, each p; is an integer and 1 < p; < 100 for every i.
4a.
Show that there exists i and j with i + j such that p; divides p;.
4b.
Show that there exists i and j with i < j such that the consecutive sum p;+Pi+1+…+Pj
is divisible by 37.
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