Intereting Posts

Number of primitive characters modulo $m$.
Algorithms for solving the discrete logarithm $a^x \equiv b\pmod{n}$ when $\gcd(a,n) \neq 1$
How to find an integer solution for general Diophantine equation ax + by + cz + dt… = N
Gödel's Incompleteness Theorem – Diagonal Lemma
Proving $\sqrt{a+\sqrt{b}}=\sqrt{m}+\sqrt{n}\iff a^{2}-b$ is a square
On Spec of a localized ring
Graph Run Time, Nodes and edges.
Probability that all bins contain strictly more than one ball?
How many distinct ways to climb stairs in 1 or 2 steps at a time?
what is the definition of $=$?
Throwing $k$ balls into $n$ bins.
The derivative of $e^x$ using the definition of derivative as a limit and the definition $e^x = \lim_{n\to\infty}(1+x/n)^n$, without L'Hôpital's rule
Why does the semigroup commute with integration?
Method of characteristics. Small question about initial conditions.
Finding Galois group of $K=\Bbb{Q}(\omega,\sqrt2)$, showing that $K=\Bbb{Q}(\omega\sqrt2)$, and finding $\operatorname{min}(\omega\sqrt2,\Bbb{Q})$

Let $K_n$ be a complete $n$ graph with a color set $c$ with $c=\{\text{Red}, \text{Blue}\}$. Every edge of the complete $n$ graph is colored either $\text{Red}$ or $\text{Blue}$. Since $R(3, 3)=6$, the $K_6$ graph must contain at least one monochromatic $K_3$ graph. How can I prove that this graph must contain another (different) monochromatic $K_3$ graph. I saw proofs which uses the fact that there are at most $18$ non-monochromatic $K_3$ graphs. Since there are $20$ $K_3$ graphs (how can you calculate this) there are at least 2 monochromatic $K_3$ graphs. Are there other proofs?

- Proving that irreducibility of a matrix implies strong connectedness of the graph
- 5-color graph problem
- Prove that a simple graph with $2n$ vertices without triangles has at most $n^2$ lines.
- Moscow puzzle. Number lattice and number rearrangement. Quicker solution?
- How many connected graphs over V vertices and E edges?
- Spectrum of adjacency matrix of complete graph
- A sequence of $n^2$ real numbers which contains no monotonic subsequence of more than $n$ terms
- vertex cover , linear program extreme point
- Heuristics for topological sort
- Is there is a way to construct a covering space of a wedge of two circles for a given normal subgroup

Since $R(3,3)=6$ there is a monochromatic triangle $\Delta$. Let’s say it’s blue. Look at the other three vertices. If there is no red edge between them then we’ve found a second blue triangle, so suppose we have found a red edge $xy$, $x,y\notin\Delta$. If there are two blue edges from $x$ to $\Delta$ then we’ve found a second blue triangle, so assume there are two red edges from $x$ to $\Delta$. Similarly assume there are two red edges from $y$ to $\Delta$. But that means that there is a $z\in\Delta$ such that $xz$ and $yz$ are both red, so we’ve found a red triangle.

- Question about the independence definition.
- Homological algebra in PDE
- Need help understanding a lift of a vector field
- $\sup$, $\limsup$ or else, what is the error here?
- Rank of sum of rank-1 matrices
- how do I prove that $\mathbb{Q} /\langle x^2 – 2 \rangle$ is a field
- Need help with $\int_0^1 \frac{\ln(1+x^2)}{1+x} dx$
- Zeros of a Tropical polynomial
- Linear optimization problem.
- Prerequisites to study cohomology?
- Characterize stochastic matrices such that max singular value is less or equal one.
- If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
- Cluster points of multiples of the fractional part of an irrational number.
- Help with null hypothesis
- Alternative definition of covering spaces.