Prove or disprove that given a set of 125 integers, one can choose a subset of S of 16 of them so that the difference of any two integers in S is divisible by 8.
Prove or disprove that given a set of 125 integers, one can choose a subset of S of 16 of them so that the difference of any two integers in S is divisible by 8.
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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![**Problem Statement:**
Prove or disprove that given a set of 125 integers, one can choose a subset \( S \) of 16 of them so that the difference of any two integers in \( S \) is divisible by 8.
**Explanation:**
You have a set of 125 integers and need to identify if there exists a subset of 16 integers where the difference between any two integers is a multiple of 8. This means that every pair of integers in this subset differs by a number that can be evenly divided by 8.
Consider exploring approaches such as pigeonhole principle or modular arithmetic to tackle this problem and determine the feasibility of forming such a subset.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4e7b45d-7759-4936-874e-85be62c48a7b%2F11973531-dabb-4242-8264-8c551f382015%2F97tznnj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Prove or disprove that given a set of 125 integers, one can choose a subset \( S \) of 16 of them so that the difference of any two integers in \( S \) is divisible by 8.
**Explanation:**
You have a set of 125 integers and need to identify if there exists a subset of 16 integers where the difference between any two integers is a multiple of 8. This means that every pair of integers in this subset differs by a number that can be evenly divided by 8.
Consider exploring approaches such as pigeonhole principle or modular arithmetic to tackle this problem and determine the feasibility of forming such a subset.
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