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CF1719B Mathematical Circus
题链：cf luogu 分类讨论思想。 Description 把 \(1\) 到 \(n\) 共 \(n\) 个整数分成 \(\frac{n}{2}\) 对有序数对 \(\left(a_i, b_i\right)\)，则对于 \(\forall \left(a_i, b_i\right), 4\mid(a_i+k)\times b_i\)。问合法方案是否存在，若存在给出一组合法方案。 Analysis 既然是与CF1719B Mathematical Circus 题解
一道不错的构造题。 思路 先说一句废话，能被 \(4\) 整除的数在除以 \(2\) 之后得到的数还是一个偶数。 我们可以根据 \(k\) 的奇偶性以及 \(k\) 除以 \(2\) 之后的奇偶性分成三种情况来进行讨论。 当 \(k\) 为奇数时，我们把所有偶数都放在 \(b\) 的位置上，把所有的奇数都放在 \(a\)julia的Unicode 字符输入
来源：https://docs.julialang.org/en/v1/manual/unicode-input/ 所有的字符可在上述链接自行查看 点击具体操作可了解如何使用 Code point(s) Character(s) Tab completion sequence(s) Unicode name(s) U+000A1 ¡ \exclamdown Inverted Exclamation Mark U+000A3 £ \sterli1.2、数学基础：集合与关系 (Mathematical foundations: sets and relations)
第一章 - 算法基础与算法分析 fundamentals of algorithms and algorithm analysis 1.2、数学基础：集合与关系 (Mathematical foundations: sets and relations)1.2.1、集合、等价集合、基数(Sets, set equality, cardinality)(1)、集合(2)、等价集合(3)、空集(empty set)(4LATEX Mathematical Symbols
Markdown mathematical notation
https://latex.codecogs.com/eqneditor/editor.php 代码 结果 a+b $a+b$ x_1^2 $x_1^2$ x_{22} $x_{22}$ x^{(n)} $x^{(n)}$ ^*x^* $*x*$ \frac{x+y}{2} $\frac{x+y}{2}$ \frac{1}{1+\frac{1}{2}} $\frac{1}{1+\frac{1}{2}}$ \sqrt[3]{3} $\sqrt[3]{LaTeX中的特殊符号，数学公式符号的相关写法
文章目录 前言1、有关特殊符号 symbols2、有关数学公式相关的符号 mathematical symbols小结 前言 创作开始时间：2021年7月23日13:39:12 有时候需要在LaTeX中用到特殊符号和数学公式，所以在这里记录一下 （相当于一个cheet sheet了）。 1、有关特殊符号 symbols LATEX Mathemamatlab对图像处理的数学形态学（Mathematical Morphology）运算。
原文地址：http://blog.sina.com.cn/wind8961，参考链接 函数功能： 对二值图像进行数学形态学（Mathematical Morphology）运算。 语法格式： BW2 = bwmorph(BW,operation) 对二值图像进行指定的形态学处理。 BW2 = bwmorph(BW,operation,n) 对二值图像进行n次指定的形态学处理。 n可以CF1461F - Mathematical Expression 题解
先大力分类讨论： 有 \(\texttt +\)，此时如果有 \(\texttt-\) 它也没有用，被 \(\texttt+\) 代替会更优。 有 \(\texttt*\)，这是接下来讲的重点； 无，那就全部 \(\texttt+\)； 无，此时有 \(\texttt-\) 的话就有用了。 有 \(\texttt-\)。 有 \(\texttt*\)，这个还稍微有点东西，但也非常简单Chinese
The high-water mark高水位线、高水平线 of Chinese mathematics occurred in the 13th century during the latter half of the Song dynasty (960–1279), with the development of Chinese algebra. The most important text from that period is the Precious Mirror四元玉鉴？Chinese
An analysis of early Chinese mathematics has demonstrated论证、说明 its unique development compared to other parts of the world, leading scholars to assume an entirely independent development. The oldest extant mathematical text from China is the Zhoubi Suanjhdu 1017 A Mathematical Curiosity
Problem Description Given two integers n and m, count the number of pairs of integers (a,b) such that 0 < a < b < n and (a^2+b^2 +m)/(ab) is an integer.This problem contains multiple test cases!The first line of a multiple input is an integer N,Introduction to Mathematical Thinking-Problem 8
8.Prove that if the sequence {an}n=1∞\left\{a_n\right\}_{n=1}^\infty{an}n=1∞ tends to limit L as n→∞n \rightarrow \inftyn→∞, then for any fixed number M>0M>0M>0, the sequence {Man}n=1∞\left\{M a_n\right\}_{n=1}^\infty{Man}n=1∞ tenIntroduction to Mathematical Thinking-Problem 5
5.Prove that for any integer nnn, at least one of the integers n,n+2,n+4n, n+2, n+4n,n+2,n+4 is divisible by 3. Proof: By the Division Theorem, nnn can be expressed as either 3q3q3q, or 3q+13q+13q+1, or 3q+23q+23q+2, where qqq is an integer. If n=3qn=3qA Mathematical Olympiad Primer Ch2
Inequalities (a-b)^2 >=0 -> ab<=(a^2+b^2)/2 root(xy) <= (x+y)/2 Geometric mean <= arithmetic mean n-th root of x1x2x3...xn <= (x1+x2+x3...+xn)/n Cauchy-Schwarz inequality: a1,a2,a3,a4...an, b1,b2...bn are real numbers abs(a1b1+a2018焦作网络赛B-Mathematical Curse
B: Mathematical Curse 时间限制: 1 Sec 内存限制: 128 MB 题目描述 A prince of the Science Continent was imprisoned in a castle because of his contempt for mathematics when he was young, and was entangled in some mathematical curses. He studied hard until hMA1MSP: Mathematical and Statistical Programming
MA1MSP: Mathematical and Statistical ProgrammingAssignment 4This assignment counts to 35% of the total marks of this module. Full marks of thisassignment can be gained from complete answers to ALL questions and submitting theMATLAB files to me by email (jMathematical Functions (Transact-SQL)
Mathematical Functions (Transact-SQL) APPLIES TO: SQL Server Azure SQL Database Azure SQL Data Warehouse Parallel Data Warehouse The following scalar functions perform a calculation, usually based on input values that are provided as arguments, and开源数学软件zzllrr Mather小乐数学简介Summary
中文摘要 Summary in Chinese 基于网页编程开发经验，和对数学学科的持久热爱及钻研精神，原创开源实现一款跨平台可离线运行并满足多用户背景、多场景需要的数学专业软件：小乐数学zzllrr Mather，并在软件基础上，影响和提高全民对当今已知数学的认知，在学术界、产业界推动数学基础协