- #1
HmBe
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Homework Statement
The Attempt at a Solution
Don't have a clue how to even start this one, sorry.
HmBe said:Yeah I'm happy with the pigeon hole principle, although I can't quite see how it applies as a can be any natural number or 0, so surely the size of set A is infinite?
Prime numbers are positive integers that have exactly two divisors, 1 and itself. They cannot be divided evenly by any other number. Prime numbers are important in mathematics because they are the building blocks of all other numbers, and they have many applications in number theory, cryptography, and computer science.
The pigeonhole principle states that if there are more objects than there are spaces to put them in, at least one space must contain more than one object. It is used in mathematics to prove the existence or non-existence of solutions to certain problems, and to show that certain patterns or arrangements are inevitable.
Modular arithmetic is used in cryptography, computer science, and music theory, among other fields. In cryptography, it is used to encrypt and decrypt messages, while in computer science, it is used to optimize algorithms and data structures. In music theory, it is used to analyze and create musical scales and chords.
A prime number is a positive integer that has exactly two divisors, 1 and itself. A composite number is a positive integer that has more than two divisors. In other words, a composite number can be divided evenly by at least one number other than 1 and itself.
There are several relationships between prime numbers and modular arithmetic. For example, in modular arithmetic, the set of integers modulo a prime number forms a finite field, which has many interesting properties. Additionally, modular arithmetic can be used to find the last digit of a large power of a prime number, as well as to generate prime numbers using certain algorithms.