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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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 28E: Let and be positive integers. If and is the least common multiple of and , prove that . Note...

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Question

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.

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