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What do i really need to understand in Number theory (anyone pls)

Number Theory

24th Jan 2023, 6:01 AM
Abdul rahmon
Abdul rahmon - avatar
5 Answers
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Number theory is a broad field that encompasses many different topics, but for programming purposes, there are a few key concepts that are particularly important to understand: 1. Prime numbers: Prime numbers are positive integers that are divisible by only 1 and themselves. Understanding how to test whether a number is prime or not is important for certain types of encryption algorithms and other applications that rely on the unique properties of prime numbers. 2. Modular arithmetic: Modular arithmetic is a way of performing arithmetic operations that "wrap around" a certain value, called the modulus. For example, if you are working with numbers in the range 0-9 and you perform the operation 7 + 5, the result would be 12, but in modular arithmetic, the result would be 2 (because 12 % 10 = 2). Understanding modular arithmetic is important for understanding many encryption and compression algorithms. 3. GCD and LCM: The greatest common divisor (GCD) and least common multiple (LCM) of two or more numbers are important concepts in number theory. The GCD is the largest positive integer that divides both numbers without a remainder, and the LCM is the smallest positive integer that both numbers divide without a remainder. These concepts are important for various algorithms such as the Euclidean algorithm for finding the GCD and the Chinese Remainder Theorem. 4. Euler's Totient function: Euler's Totient function is a function that gives the number of integers between 1 and a given number n that are relatively prime to n. It's an important concept in number theory, and it's used in various algorithms such as the RSA encryption. 5. Diophantine equations: A Diophantine equation is an equation where the solutions are integers. Understanding how to solve Diophantine equations is important for some cryptographic algorithms, such as the ElGamal encryption. These are just a few examples of the concepts in number theory that are important for programming. Depending on the specific application or algorithm you are working
24th Jan 2023, 7:05 AM
Mirielle
Mirielle - avatar
+ 3
So many languages were tagged and yet the question was about number theory. As important as it may be, the post bears no language specific topic.
24th Jan 2023, 7:48 AM
Ipang
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Number theory is mostly found in competitive programming, in my opinion it is not that useful in other types of programming, if you still want to learn some number theory I think the most useful would be sequences and mathematical induction, euclidean algorithm and maybe Sieve of Eratosthenes
24th Jan 2023, 6:31 AM
Snapfire
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Ipang I just want to understand the basic (concept) and i found that Number Theory is mostly about logic (it was not about programming language)
24th Jan 2023, 9:27 AM
Abdul rahmon
Abdul rahmon - avatar
0
Wath is articale
24th Jan 2023, 4:34 PM
Alemseged AS
Alemseged AS - avatar