PLEASE WRITE FULL STEPS , THANK YOU 4c.Suppose that pi, P2, ..., P51 are all distinct and 1 < Pi < 86 for every i. Show thatthere exists i and j such that pi – Pj - 16. 4There are 51 software students taking MATH 211. Let p1, P2, ..., P51 be their finalexam 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+…+Pjis divisible by 37.

Given that p1, p2, p3,..., p51 are the final exam scores of 51 software students who are taking MATH…

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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.1: Postulates For The Integers (optional)

Problem 25E: 25. Prove that if and are integers and, then either or. (Hint: If, then either or, and similarly...

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Question

PLEASE WRITE FULL STEPS , THANK YOU

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.

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