4) A is a set of m 2 1 positive integers. Show that exists a non-empty subset BCA such that the sum of all elements of B is divisible by m. [Suggestion: Considering A= {a, a, ., am}, suppose that no sum of the form a1 + a2 + . + ak,1sksm, is divisible by m]

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 3E
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4) A is a set of m 21 positive integers. Show that exists a non-empty subset
BCA such that the sum of all elements of B is divisible by m.
[Suggestion: Considering A= {a, a, ., am}, suppose that no sum of the form
a1 + a2 +... + ak,
1sksm, is divisible by m]
Transcribed Image Text:4) A is a set of m 21 positive integers. Show that exists a non-empty subset BCA such that the sum of all elements of B is divisible by m. [Suggestion: Considering A= {a, a, ., am}, suppose that no sum of the form a1 + a2 +... + ak, 1sksm, is divisible by m]
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