数学代写代考| Discrete Mathematics 离散数学代写 - 代考代写：100%准时可靠您的作业代写专家

Number theory is the branch of mathematics that is concerned with the mathematical properties of the natural numbers and integers. These include properties such as the parity of a number; divisibility; additive and multiplicative properties; whether a number is prime or composite; the prime factors of a number; the greatest common divisor and least common multiple of two numbers; and so on.

Number theory has many applications in computing including cryptography and coding theory. For example, the RSA public key cryptographic system relies on its security due to the infeasibility of the integer factorization problem for large numbers.

There are several unsolved problems in number theory and especially in prime number theory. For example, Goldbach’s ${ }^{1}$ conjecture states that every even integer greater than two is the sum of two primes, and this result has not been proved to date. Fermat’s ${ }^{2}$ Last Theorem (Fig. 3.1) states that there is no integer solution to $x^{n}+y^{n}=z^{n}$ for $n>2$, and this result remained unproved for over 300 years until Andrew Wiles finally proved it in the mid-1990s.

The natural numbers $\mathbb{N}$ consist of the numbers ${1,2,3, \ldots}$. The integer numbers $\mathbb{Z}$ consist of ${\ldots-2,-1,0,1,2, \ldots}$. The rational numbers $\mathbb{Q}$ consist of all the numbers of the form $\left{{ }^{p} /_{q}\right.$ where $p$ and $q$ are integers and $\left.q \neq 0\right}$. The real numbers $\mathbb{R}$ is defined to be the set of converging sequences of rational numbers, and they are a superset of the rational numbers. They contain the rational and irrational numbers. The complex numbers $\mathbb{C}$ consist of all the numbers of the form ${a+b i$ where $a, b \in \mathbb{R}$ and $i=\sqrt{-} 1}$.

Pythagorean triples (Fig. 3.2) are combinations of three whole numbers that satisfy Pythagoras’ equation $x^{2}+y^{2}=z^{2}$. There are an infinite number of such triples, and an example of such a triple is $3,4,5$ since $3^{2}+4^{2}=5^{2}$.

The Pythagoreans discovered the mathematical relationship between the harmony of music and numbers, and their philosophy was that numbers are hidden in everything from music to science and nature. This led to their philosophy that “everything is number”.

图论代考

自然数 $\mathbb{N}$ 由数字 $\{1,2,3, \ldots\}$ 组成。整数 $\mathbb{Z}$ 由 $\{\ldots-2,-1,0,1,2, \ldots\}$ 组成。有理数 $\mathbb{Q}$ 由 $\left\{{ }^{p} /_{q}\right.$ 形式的所有数字组成，其中 $p$ 和 $q$ 是整数，$ \left.q \neq 0\right\}$。实数 $\mathbb{R}$ 被定义为有理数收敛序列的集合，它们是有理数的超集。它们包含有理数和无理数。复数 $\mathbb{C}$ 由 $\{a+bi$ 形式的所有数字组成，其中 $a, b \in \mathbb{R}$ 和 $i=\sqrt{-} 1\}美元。毕达哥拉斯三元组（图 3.2）是满足毕达哥拉斯方程 $x^{2}+y^{2}=z^{2}$ 的三个整数的组合。有无数个这样的三元组，这种三元组的一个例子是 $3,4,5$，因为 $3^{2}+4^{2}=5^{2}$。毕达哥拉斯学派发现了音乐和数字之间的数学关系，他们的哲学是数字隐藏在从音乐到科学和自然的一切事物中。这导致了他们的哲学，即“一切都是数字”。

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Cryptosystem
A system that describes how to encrypt or decrypt messages
Plaintext
Message in its original form
Ciphertext
Message in its encrypted form
Cryptographer
Invents encryption algorithms
Cryptanalyst
Breaks encryption algorithms or implementations

编码理论代写

编码理论（英语：Coding theory）是研究编码的性质以及它们在具体应用中的性能的理论。编码用于数据压缩、加密、纠错，最近也用于网络编码中。不同学科（如信息论、电机工程学、数学、语言学以及计算机科学）都研究编码是为了设计出高效、可靠的数据传输方法。这通常需要去除冗余并校正（或检测）数据传输中的错误。

编码共分四类：^[1]