Intereting Posts

On a unique(?) binomial property of $3003$
Inductive definition of power set for finite sets
Why do we need an integral to prove that $\frac{22}{7} > \pi$?
Principal ideal ring
Generalized convex combination over a Banach space
converge and converge absolutely of a series
Density of irrationals
For $f\in\mathbb{Q}$, Gal($f)\subset S_n$ is a subset of $A_n$ iff $\Delta(f)$ is a square in $\mathbb{Q}^*$
For $N\unlhd G$ , with $C_G(N)\subset N$ we have $G/N$ is abelian
What is the “taxonomy” or “hierarchy” (partial ordering) of algebraic objects used to attempt to capture geometric intuition?
Analytic Capacity
How do you go about learning mathematics?
Why is Gimbal Lock an issue?
Positive integers $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}} > 1$ satisfying $\sum_{i = 1}^{n} p_{i}^{-r_{i}} < 1$
1-separated sequences of unit vectors in Banach spaces

I have to use Fermat’s little theorem to find the value of$$

x \uparrow \uparrow k \mod m = \underbrace{x^{x^{{}^{{{.\,}^{.\,^{.\,^{x}}}}}}}}_{k\text{ times}} \mod m,$$

where $x$ is repeated in power $k-1$ times and $m$ is any number.

That is, if $x=5$, $k=3$ and $m=3$, then I need to find $\ 5^{5^5} \mod 3$ .

Also note that $x$ is always a prime number.

- Greatest common divisor is the smallest positive number that can be written as $sa+tb$
- When can you simplify the modulus? ($10^{5^{102}} \text{ mod } 35$)
- A binary quadratic form: $nx^2-y^2=2$
- Infinitely many primes of the form $pn+1$
- If a number can be expressed as a product of n unique primes…
- product is twice a square

It has been in my mind for quite a while now I can’t find an answer.

- How to prove that $\frac{a+b}{2} \geq \sqrt{ab}$ for $a,b>0$?
- Is $7k-9$ ever a power of $2$?
- Divisibility Rule for 9
- Proving that $x$ is an integer, if the differences between any two of $x^{1919}$, $x^{1960}$, and $x^{2100}$ are integers
- find a parametric solutions for a special equation
- The modular curve X(N)
- How to find solutions of linear Diophantine ax + by = c?
- For $n \in \mathbb{N}$ $\lfloor{\sqrt{n} + \sqrt{n+1}\rfloor} = \lfloor{\sqrt{4n+2}\rfloor}$
- $a\mid b$ if and only if $ac \mid bc$ where $c\neq 0$
- Prove that $\frac{(n!)!}{(n!)^{(n-1)!}} $ is always an integer.

$x \uparrow \uparrow k \mod m = x^{x \uparrow \uparrow (k-1) \mod \phi(m)} \mod m$.

Which is $O(k)$ repeating process.

- Generating Pythagorean triples for $a^2+b^2=5c^2$?
- $g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
- Find the particular solution of $u_x+2u_y-4u=e^{x+y}$ satisfying the following side condition $u(x,-x) = x$
- How to solve for a variable that is only in exponents?
- Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
- Can all math results be formalized and checked by a computer?
- How do i calculate Dice probability
- A problem on Number theory
- To compute $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2|^2 dz$ where $\mathcal{C}$ is the unit circle in $\mathbb{C}$
- Can a space $X$ be homeomorphic to its twofold product with itself, $X \times X$?
- How to solve this trig integral?
- Differentiation operator is closed?
- A less challenging trivia problem
- Quadruple of Pythagorean triples with same area
- Given a rational number $x$ and $x^2 < 2$, is there a general way to find another rational number $y$ that such that $x^2<y^2<2$?