MY-ASSIGNMENTEXPERT™可以为您提供math Math46400 Number theory 数论的代写代考和辅导服务！
这是纽约市立学院数论课程的代写成功案例。
Math46400简介
A first course in algebraic number theory which assumes some abstract algebra. Topics include: unique factorization in the integers and Euclidean domains, structure of the groups Z/mZ and their multiplicative units, quadratic residues and quadratic reciprocity, algebraic number fields, finite fields.
Prerequisites: Grade of C or better in MATH 34700 or departmental permission.
Contact Hours: 4 hr./wk.
Credits: 4
This is an undergraduate version of Math A6400. You must take the graduate version if you want graduate credit.
Prerequisites
Number theory or arithmetic or higher arithmetic in older usage is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, “Mathematics is the queen of the sciences—and number theory is the queen of mathematics.”
Math46400 Number theory HELP（EXAM HELP， ONLINE TUTOR）
Computational Problem 1
Suppose $n$ is the product of three positive consecutive integers and that $n$ is divisible by 7 . Which of the following is not necessarily a divisor of $n$ ? Justify your reasoning for full credit.
$\begin{array}{lllll}6 & 14 & 21 & 28 & 42\end{array}$
Computational Problem 2
Consider the situation where the positive integer $a$ is divided by the positive integer $b$ using the Division Algorithm (see Theorem 5.8 in our book) yielding
$$
a=652 \cdot b+8634
$$
By how much can we increase both $a$ and $b$ by the same amount without changing the quotient $q=652$ ?
Computational Problem 3
Compute $\operatorname{gcd}(a, b)$ using the Euclidean algorithm then use the definition of least common multiple to compute $\operatorname{lcm}(a, b)$ for $a=39$ and $b=144$. Finally, show that
$$
\operatorname{gcd}(a, b) \cdot \operatorname{lcm}(a, b)=a \cdot b
$$
holds true for $a=39$ and $b=144$.
Computational Problem 4
Use the Euclidean Algorithm to find integers $x$ and $y$ satisfying $\operatorname{gcd}(24,138)=24 x+138 y$.
Computational Problem 5
Solve the Diophantine equation
$$
24 x+138 y=18
$$
That is, find ALL integer solutions. Lastly, explain why $24 x+138 y=16$ has no integer solutions.
MY-ASSIGNMENTEXPERT™可以为您提供MATH MATH46400 NUMBER THEORY 数论的代写代考和辅导服务！
