SlideShare a Scribd company logo
1 of 1
Download to read offline
Prove. Let n be a natural number. Any set of n integers {a1, a2, . . . , an} for which no two are
congruent modulo n is a complete residue system modulo n.
Solution
There are n distinct residues in complete residue system
Since given set have n integers and no two are congruent modulo n hence we have a set of n
distinct residues modulo n.
ANd hence the given set is a complete residue system modulo n

More Related Content

More from shahidqamar17

ROT13 (rotate by 13 places) is a simple letter substitution cipher t.pdf
ROT13 (rotate by 13 places) is a simple letter substitution cipher t.pdfROT13 (rotate by 13 places) is a simple letter substitution cipher t.pdf
ROT13 (rotate by 13 places) is a simple letter substitution cipher t.pdf
shahidqamar17
 
question.(player, entity ,field and base.java codes are given)Stop.pdf
question.(player, entity ,field and base.java codes are given)Stop.pdfquestion.(player, entity ,field and base.java codes are given)Stop.pdf
question.(player, entity ,field and base.java codes are given)Stop.pdf
shahidqamar17
 
1Write a Java program that calculates and displays the Fibonacciseri.pdf
1Write a Java program that calculates and displays the Fibonacciseri.pdf1Write a Java program that calculates and displays the Fibonacciseri.pdf
1Write a Java program that calculates and displays the Fibonacciseri.pdf
shahidqamar17
 
need an example of a System Anaysis and design project must have 3 .pdf
need an example of a System Anaysis and design project must have 3 .pdfneed an example of a System Anaysis and design project must have 3 .pdf
need an example of a System Anaysis and design project must have 3 .pdf
shahidqamar17
 
Money laundering has become a mechanism for terrorist financing acti.pdf
Money laundering has become a mechanism for terrorist financing acti.pdfMoney laundering has become a mechanism for terrorist financing acti.pdf
Money laundering has become a mechanism for terrorist financing acti.pdf
shahidqamar17
 
1. What is the purpose of level numbers in COCOL records2.What ar.pdf
1. What is the purpose of level numbers in COCOL records2.What ar.pdf1. What is the purpose of level numbers in COCOL records2.What ar.pdf
1. What is the purpose of level numbers in COCOL records2.What ar.pdf
shahidqamar17
 
Identify the main issues in Urban Transport Planning in Africa. What.pdf
Identify the main issues in Urban Transport Planning in Africa. What.pdfIdentify the main issues in Urban Transport Planning in Africa. What.pdf
Identify the main issues in Urban Transport Planning in Africa. What.pdf
shahidqamar17
 
How many parties are needed to create an estate A trust Identify t.pdf
How many parties are needed to create an estate A trust Identify t.pdfHow many parties are needed to create an estate A trust Identify t.pdf
How many parties are needed to create an estate A trust Identify t.pdf
shahidqamar17
 

More from shahidqamar17 (20)

The LabVIEW G programming is considered to be a data flow programmin.pdf
The LabVIEW G programming is considered to be a data flow programmin.pdfThe LabVIEW G programming is considered to be a data flow programmin.pdf
The LabVIEW G programming is considered to be a data flow programmin.pdf
 
what is a bottom heap up construction with an example pleaseSol.pdf
what is a bottom heap up construction with an example pleaseSol.pdfwhat is a bottom heap up construction with an example pleaseSol.pdf
what is a bottom heap up construction with an example pleaseSol.pdf
 
What are the types of differences that exist between IFRS and U.S. G.pdf
What are the types of differences that exist between IFRS and U.S. G.pdfWhat are the types of differences that exist between IFRS and U.S. G.pdf
What are the types of differences that exist between IFRS and U.S. G.pdf
 
ROT13 (rotate by 13 places) is a simple letter substitution cipher t.pdf
ROT13 (rotate by 13 places) is a simple letter substitution cipher t.pdfROT13 (rotate by 13 places) is a simple letter substitution cipher t.pdf
ROT13 (rotate by 13 places) is a simple letter substitution cipher t.pdf
 
question.(player, entity ,field and base.java codes are given)Stop.pdf
question.(player, entity ,field and base.java codes are given)Stop.pdfquestion.(player, entity ,field and base.java codes are given)Stop.pdf
question.(player, entity ,field and base.java codes are given)Stop.pdf
 
Question 25 A Multilateral agreement in which countries signed to ban.pdf
Question 25 A Multilateral agreement in which countries signed to ban.pdfQuestion 25 A Multilateral agreement in which countries signed to ban.pdf
Question 25 A Multilateral agreement in which countries signed to ban.pdf
 
1Write a Java program that calculates and displays the Fibonacciseri.pdf
1Write a Java program that calculates and displays the Fibonacciseri.pdf1Write a Java program that calculates and displays the Fibonacciseri.pdf
1Write a Java program that calculates and displays the Fibonacciseri.pdf
 
need an example of a System Anaysis and design project must have 3 .pdf
need an example of a System Anaysis and design project must have 3 .pdfneed an example of a System Anaysis and design project must have 3 .pdf
need an example of a System Anaysis and design project must have 3 .pdf
 
Money laundering has become a mechanism for terrorist financing acti.pdf
Money laundering has become a mechanism for terrorist financing acti.pdfMoney laundering has become a mechanism for terrorist financing acti.pdf
Money laundering has become a mechanism for terrorist financing acti.pdf
 
Let x be any set and let lambda SolutionProof. Obviously .pdf
Let x be any set and let lambda SolutionProof. Obviously .pdfLet x be any set and let lambda SolutionProof. Obviously .pdf
Let x be any set and let lambda SolutionProof. Obviously .pdf
 
Java public cts Node t next ni next SolutionYou hav.pdf
Java public cts Node t next ni next SolutionYou hav.pdfJava public cts Node t next ni next SolutionYou hav.pdf
Java public cts Node t next ni next SolutionYou hav.pdf
 
1. What is the purpose of level numbers in COCOL records2.What ar.pdf
1. What is the purpose of level numbers in COCOL records2.What ar.pdf1. What is the purpose of level numbers in COCOL records2.What ar.pdf
1. What is the purpose of level numbers in COCOL records2.What ar.pdf
 
In Android Applications,A resource identifier is a unique number t.pdf
In Android Applications,A resource identifier is a unique number t.pdfIn Android Applications,A resource identifier is a unique number t.pdf
In Android Applications,A resource identifier is a unique number t.pdf
 
If primarily illegal aliens fill menial and dirty jobs that American.pdf
If primarily illegal aliens fill menial and dirty jobs that American.pdfIf primarily illegal aliens fill menial and dirty jobs that American.pdf
If primarily illegal aliens fill menial and dirty jobs that American.pdf
 
Implement the findPre function of the LinkedList class .Node Lin.pdf
Implement the findPre function of the LinkedList class .Node  Lin.pdfImplement the findPre function of the LinkedList class .Node  Lin.pdf
Implement the findPre function of the LinkedList class .Node Lin.pdf
 
Identify the main issues in Urban Transport Planning in Africa. What.pdf
Identify the main issues in Urban Transport Planning in Africa. What.pdfIdentify the main issues in Urban Transport Planning in Africa. What.pdf
Identify the main issues in Urban Transport Planning in Africa. What.pdf
 
Hwk due June 5th e June 5th Help I Grace Period 14 days left Regis.pdf
Hwk due June 5th e June 5th Help I Grace Period 14 days left  Regis.pdfHwk due June 5th e June 5th Help I Grace Period 14 days left  Regis.pdf
Hwk due June 5th e June 5th Help I Grace Period 14 days left Regis.pdf
 
How many parties are needed to create an estate A trust Identify t.pdf
How many parties are needed to create an estate A trust Identify t.pdfHow many parties are needed to create an estate A trust Identify t.pdf
How many parties are needed to create an estate A trust Identify t.pdf
 
Form 1023 Checklist does NOT include _________A. Employer Identifica.pdf
Form 1023 Checklist does NOT include _________A. Employer Identifica.pdfForm 1023 Checklist does NOT include _________A. Employer Identifica.pdf
Form 1023 Checklist does NOT include _________A. Employer Identifica.pdf
 
how important is Conscientiousness to an accounting career please e.pdf
how important is Conscientiousness to an accounting career please e.pdfhow important is Conscientiousness to an accounting career please e.pdf
how important is Conscientiousness to an accounting career please e.pdf
 

Recently uploaded

會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
中 央社
 
SURVEY I created for uni project research
SURVEY I created for uni project researchSURVEY I created for uni project research
SURVEY I created for uni project research
CaitlinCummins3
 

Recently uploaded (20)

OS-operating systems- ch05 (CPU Scheduling) ...
OS-operating systems- ch05 (CPU Scheduling) ...OS-operating systems- ch05 (CPU Scheduling) ...
OS-operating systems- ch05 (CPU Scheduling) ...
 
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
 
male presentation...pdf.................
male presentation...pdf.................male presentation...pdf.................
male presentation...pdf.................
 
MOOD STABLIZERS DRUGS.pptx
MOOD     STABLIZERS           DRUGS.pptxMOOD     STABLIZERS           DRUGS.pptx
MOOD STABLIZERS DRUGS.pptx
 
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjj
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjjStl Algorithms in C++ jjjjjjjjjjjjjjjjjj
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjj
 
The Liver & Gallbladder (Anatomy & Physiology).pptx
The Liver &  Gallbladder (Anatomy & Physiology).pptxThe Liver &  Gallbladder (Anatomy & Physiology).pptx
The Liver & Gallbladder (Anatomy & Physiology).pptx
 
Supporting Newcomer Multilingual Learners
Supporting Newcomer  Multilingual LearnersSupporting Newcomer  Multilingual Learners
Supporting Newcomer Multilingual Learners
 
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
 
An Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge AppAn Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge App
 
Including Mental Health Support in Project Delivery, 14 May.pdf
Including Mental Health Support in Project Delivery, 14 May.pdfIncluding Mental Health Support in Project Delivery, 14 May.pdf
Including Mental Health Support in Project Delivery, 14 May.pdf
 
SURVEY I created for uni project research
SURVEY I created for uni project researchSURVEY I created for uni project research
SURVEY I created for uni project research
 
e-Sealing at EADTU by Kamakshi Rajagopal
e-Sealing at EADTU by Kamakshi Rajagopale-Sealing at EADTU by Kamakshi Rajagopal
e-Sealing at EADTU by Kamakshi Rajagopal
 
How to Manage Website in Odoo 17 Studio App.pptx
How to Manage Website in Odoo 17 Studio App.pptxHow to Manage Website in Odoo 17 Studio App.pptx
How to Manage Website in Odoo 17 Studio App.pptx
 
The Story of Village Palampur Class 9 Free Study Material PDF
The Story of Village Palampur Class 9 Free Study Material PDFThe Story of Village Palampur Class 9 Free Study Material PDF
The Story of Village Palampur Class 9 Free Study Material PDF
 
OSCM Unit 2_Operations Processes & Systems
OSCM Unit 2_Operations Processes & SystemsOSCM Unit 2_Operations Processes & Systems
OSCM Unit 2_Operations Processes & Systems
 
Improved Approval Flow in Odoo 17 Studio App
Improved Approval Flow in Odoo 17 Studio AppImproved Approval Flow in Odoo 17 Studio App
Improved Approval Flow in Odoo 17 Studio App
 
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptxAnalyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
 
Mattingly "AI and Prompt Design: LLMs with NER"
Mattingly "AI and Prompt Design: LLMs with NER"Mattingly "AI and Prompt Design: LLMs with NER"
Mattingly "AI and Prompt Design: LLMs with NER"
 
UChicago CMSC 23320 - The Best Commit Messages of 2024
UChicago CMSC 23320 - The Best Commit Messages of 2024UChicago CMSC 23320 - The Best Commit Messages of 2024
UChicago CMSC 23320 - The Best Commit Messages of 2024
 
Trauma-Informed Leadership - Five Practical Principles
Trauma-Informed Leadership - Five Practical PrinciplesTrauma-Informed Leadership - Five Practical Principles
Trauma-Informed Leadership - Five Practical Principles
 

Prove. Let n be a natural number. Any set of n integers {a1, a2, . ..pdf

  • 1. Prove. Let n be a natural number. Any set of n integers {a1, a2, . . . , an} for which no two are congruent modulo n is a complete residue system modulo n. Solution There are n distinct residues in complete residue system Since given set have n integers and no two are congruent modulo n hence we have a set of n distinct residues modulo n. ANd hence the given set is a complete residue system modulo n