Intereting Posts

How badly can Dini's theorem fail if the p.w. limit isn't continuous?
How fundamental is the fundamental theorem of algebra?
construct circle tangent to two given circles and a straight line
Compactness in the weak* topology
Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$
The integral of a closed form along a closed curve is proportional to its winding number
How to prove the distributive property without using truth tables?
cutoff function vs mollifiers
A mouse leaping along the square tile
Find a solution: $3(x^2+y^2+z^2)=10(xy+yz+zx)$
Proof of the Banach–Alaoglu theorem
suppose $|a|<1$, show that $\frac{z-a}{1-\overline{a}z}$ is a mobius transformation that sends $B(0,1)$ to itself.
What is the role of Topology in mathematics?
Unique factorization domain that is not a Principal ideal domain
$ \sum _{n=1}^{\infty} \frac 1 {n^2} =\frac {\pi ^2}{6} $ then $ \sum _{n=1}^{\infty} \frac 1 {(2n -1)^2} $

Let $d > 0$ be square-free. Let $\epsilon = x_0 + y_0 \sqrt{d}$ be the minimal solution to the Pell’s equation $x ^ 2 – d y ^ 2 = 1$. Let $x + y \sqrt{d} = \epsilon ^ l, l \geq 1$ be a solution.

Question: If all the prime divisors of $x$ divides $x_0$, does it follow that $l = 1$, i.e. $x + y \sqrt{d} = x_0 + y_0 \sqrt{d}$ (or in other words, $x + y \sqrt{d}$ is the minimal solution) ?

- Solve $3x^2-y^2=2$ for Integers
- Formula : (Exact) Sum of $1^1+2^2+3^3+..+n^n$ (modulo $10^m$) with relatively small $m$
- $n!+1$ being a perfect square
- Number of Solutions to a Diophantine Equation
- Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
- On Diophantine equations of the form $x^4-n^2y^4=z^2$

- Solve the equation $(2^m-1) = (2^n-1)k^2$
- Trying to solve the equation $\sum_{i=0}^{t}(-1)^i\binom{m}{i}\binom{n-m}{t-i}=0 $ for non-negative integers $m,n,t$
- Finding a Pythagorean triple $a^2 + b^2 = c^2$ with $a+b+c=40$
- Representation of a number as a sum of squares.
- Does the equation $a^{2} + b^{7} + c^{13} + d^{14} = e^{15}$ have a solution in positive integers
- Second longest prime diagonal in the Ulam spiral?
- On the complete solution to $x^2+y^2=z^k$ for odd $k$?
- Are Euclid numbers squarefree?
- A Tale of Two Quadratic Identities (Pell-like)
- Integer solutions of $3a^2 - 2a - 1 = n^2$

- solution of differential equation $\left(\frac{dy}{dx}\right)^2-x\frac{dy}{dx}+y=0$
- Bell numbers and moments of the Poisson distribution
- Proving the Kronecker Weber Theorem for Quadratic Extensions
- Proving a formula related with zeta function
- Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
- Show that $f(x)\equiv 0$ if $ \int_0^1x^nf(x)\,dx=0$
- Calculate Laurent series for $1/ \sin(z)$
- Some intuition about embedding of $L^p$ spaces
- bound on the cardinality of the continuum? I hope not
- Proof about cubic $t$-transitive graphs
- General Integral Formula
- Prove that $1 + 4 + 7 + · · · + 3n − 2 = \frac {n(3n − 1)}{2}$
- Understanding big O notation
- What kind of matrix norm satisifies $\text {norm} (A*B)\leq \text {norm} (A)*\text {norm} (B)$ in which A is square?
- $\mathbb R = X^2$ as a Cartesian product