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Consider (A) a set of m 21 positive integers. Show that there is a non-empty subset BCA, such that, the sum of all elements of B is divisible by m'. Suggestion: A = {a1,a2, .,am}, suppose that none sum of the form a, + .+ax, 1sk sm, is divisible by m.

Consider (A) a set of m 21 positive integers. Show that there is a non-empty subset BCA, such that, the sum of all elements of B is divisible by m'. Suggestion: A = {a1,a2, .,am}, suppose that none sum of the form a, + .+ax, 1sk sm, is divisible by m.

Elements Of Modern Algebra
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 12E: Let A be a set of integers closed under subtraction. a. Prove that if A is nonempty, then 0 is in A....
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Group 2 Consider (A) a set of m 21 positive integers. Show that there is a non-empty subset BCA, such that, the sum of all elements of Bis divisible by m'. * Suggestion: A = {a1, a2, .,am}, suppose that none sum of the form a+.tax, 1sk sm, is divisible by m.
Transcribed Image Text:Group 2 Consider (A) a set of m 21 positive integers. Show that there is a non-empty subset BCA, such that, the sum of all elements of Bis divisible by m'. * Suggestion: A = {a1, a2, .,am}, suppose that none sum of the form a+.tax, 1sk sm, is divisible by m.
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