It's a well known fact that Euclidean domains are principal ideal domain by taking the element in a certain ideal with smallest \varphi value. Yet the converse is false, and one counterexample just lies among our familiar algebraic integer rings, \……

题目背景 为证一个非零吃大师 题面 Assuming AC, prove that for a integral domain R, if any nonzero prime ideal P contains a nonzero prime (p), R is UFD. 先想再看提示哦 提示 Let S be the set of elements that are prime factori……

This proof is due to Choudum. A sequence of nonnegative integers (d_1,...,d_n) is called graphic if there is a simple graph G with V(G)=\lbrace v_1,...,v_n\rbrace and d(v_i)=d_i. It's very easy to show that if a nonincreasing sequence, i.e. d_1\ge ……

飞机上半昏迷状态下以为无法调整, 暴力算出来的搞笑解答. 非常具有统计色彩 (nod) 题面 A simple graph G is called complete k-partite if there's a partion of V(G): A_1,..., A_k s.t. for all i there's no edge with both vertices in A_i , and for any v\in A……

2小时，100分满分，内容是图论，开卷，可带电子设备，可查阅课程笔记和资料，不可上网。点击长图查看：

It's a well-known fact that the alternating groups, A_n, are simple for n\neq 4, with small cases like A_1, A_2, A_3 very easy to verify. Yet most proofs of n\geq 5, including Hungerford's, relies heavily on 'magical' permutation composition, which……

思考题 from Maths homework again... 数学小题两道 Problem A You are given a bipartite graph G, find a proper coloring of the complement of G that uses minimum colors. |G|\leq 100 Problem B Given integer N. Find any n\geq N such that n+\varphi(n) is ……

This proof is due to Arturo Magidin. In category theory, as we don't consider the 'internal structure' of objects, many properties of maps are defined in an abstract way using interaction with other morphisms. 'Epimorphism' is such an analog of sur……

Solved! Difficulty: Div2C :O 竟然有60期了！！ 本期题目来源于Group Theory作业，，，难度不高 Congratulations on the 60th entry!! This problem is from my Group Theory homework (not very hard). Z(Sym(n))=ONE In the world of MATHS, a permutation i……

题目背景 证明连续性时缩放水平哈哈了(sweatgrinning) 题面 f is a nonconstant holomorphic function on a region \Omega_1 and g is defined on f(\Omega_1). Prove that if h=g\circ f is holomorphic, then so is g. 先想再看提示哦 提……