How to Solve a Modular Arithmetic Equation

Thread starter viviane363
Start date Oct 20, 2009
Tags

Cryptology Number theory Theory

In summary, Cryptology is the study of codes, ciphers, and secret communication while Number Theory is the branch of mathematics that deals with the properties of numbers and their relationships. These two fields are closely related as Number Theory provides the foundation for encryption algorithms used in Cryptology, and Cryptology uses Number Theory to break codes. Cryptology and Number Theory are important in ensuring the security and confidentiality of sensitive information in various fields, and they protect information by using mathematical algorithms to scramble data. Real-world applications of Cryptology and Number Theory include secure messaging, online banking and shopping, password protection, data encryption, electronic voting, and protecting sensitive information in the healthcare industry.

Oct 20, 2009

viviane363

Homework Statement

compute 59x +15 [tex]\equiv[/tex] 6 mod 811

Homework Equations

The Attempt at a Solution

59x [tex]\equiv[/tex] -9 mod 811
I really don't know hoow to do from here.

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Oct 20, 2009

lanedance

Homework Helper

so i think 2 numbers a,b are equivalent in modular arthimetic, mod n, if

a-b = m*n for some integer m

in your case this translates to
59x+9 = 811.m

Related to How to Solve a Modular Arithmetic Equation

1. What is Cryptology and Number Theory?

Cryptology is the study of codes, ciphers, and secret communication. Number theory is the branch of mathematics that deals with the properties of numbers and their relationships. In combination, these two fields are used to create and break codes and ensure the security of information.

2. How are Cryptology and Number Theory related?

Number theory provides the mathematical foundation for many encryption algorithms used in cryptology. It involves concepts such as prime numbers, modular arithmetic, and discrete logarithms, which are crucial in creating secure codes. Cryptology also uses number theory to analyze and break existing codes.

3. What is the importance of Cryptology and Number Theory?

Cryptology and number theory play a critical role in ensuring the security and confidentiality of sensitive information in various fields such as military, finance, and communication. They are also used in data protection and privacy, cybersecurity, and digital signatures.

4. How does Cryptology and Number Theory protect information?

Cryptology and number theory use mathematical algorithms to scramble data into an unreadable format, making it difficult for unauthorized individuals to access or understand. Only individuals with the correct key or code can decipher the information.

5. What are some real-world applications of Cryptology and Number Theory?

Cryptology and number theory have numerous practical applications, including secure messaging, online banking and shopping, password protection, and data encryption in databases. They are also used in electronic voting, secure communication between government agencies, and in protecting sensitive information in the healthcare industry.