Intereting Posts

Monotone class theorem vs Dynkin $\pi-\lambda$ theorem
Can all real/complex vector spaces be equipped with a Hilbert space structure?
Regular way to fill a $1\times1$ square with $\frac{1}{n}\times\frac{1}{n+1}$ rectangles?
Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
Counting the number of integers $i$ such that $\sigma(i)$ is even.
Exponential map of Beltrami-Klein model of hyperbolic geometry
Normal, Non-Metrizable Spaces
Infinite limits
Proving that the coefficients of the characteristic polynomial are the traces of the exterior powers
Subgroup of a Finite Group
Using Fermat's Little Theorem, find the least positive residue of $3^{999999999}\mod 7$
Approximating a three-times differentiable function by a linear combination of derivatives
Let graph $G = (V, E)$ $\Rightarrow$ $\alpha(G) \ge \frac{{|V|}^{2}}{2 \times (|E| + |V|)}$
Connecting $\sum\limits_{n=0}^\infty\frac{n!\,(2n)!}{(3n+2)!}$ and $\sum\limits_{n=1}^\infty\frac{1}{n \binom{3n}{n}}$
Boundary/interior of $0$-simplex

$\phi(\pi(\phi^\pi)) = 1$

I saw it on an expired flier for a lecture at the university. I don’t know what $\phi$ is, so I tried asking Wolfram Alpha to solve $x \pi x^\pi = 1$ and it gave me a bunch of results with $i$, and I don’t know what that is either.

- How to use Fermat's little theorem to find $50^{50}\pmod{13}$?
- Is $n=1073$ a strong pseudoprime to bases $a=260, 813?$
- Primes $p$ such that $3$ is a primitive root modulo $p$ , where $p=16 \cdot n^4+1$?
- Modulo of a negative number
- Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.
- Find the $least$ number $N$ such that $N=a^{a+2b} = b^{b+2a}, a \neq b$.

- What does **Ens** stand for?
- Congruence Equation $3n^3+12n^2+13n+2\equiv0,\pmod{2\times3\times5}$
- Divisibility for 7
- how to calculate $10^{31}$ mod $67$.
- Proving the so-called “Well Ordering Principle”
- Prove that two distinct number of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $gcd=2$ if $a$ is odd
- How can I show that $n! \leqslant (\frac{n+1}{2})^n$?
- Question about set notation: what does $]a,b[$ mean?
- How does one attack a divisibility problem like $(a+b)^2 \mid (2a^3+6a^2b+1)$?
- Does every number not ending with zero have a multiple without zero digits at all?

It’s a joke based on the use of the $\phi$ function (Euler’s totient function), the $\pi$ function (the prime counting function), the constant $\phi$ (the golden ratio), and the constant $\pi$. Note $\phi^\pi\approx 4.5$, so there are two primes less than $\phi^\pi$ (they are $2$ and $3$), so $\pi(\phi^\pi)=2$. There is only one positive integer less than or equal to $2$ which is also relatively prime to $2$ (this number is $1$), so $\phi(2)=1$. Hence we have

$$\phi(\pi(\phi^\pi))=\phi(2)=1$$

- Image of open donut under $\phi=z+\frac{1}{z}$
- Analytic solution of a system of four second order polynomials
- How to check if a function is minimum to functional?
- Factorization of ideals in $\mathbb{Z}$
- Show that sum of elements of rows / columns of a matrix is equal to reciprocal of sum of elements of rows/colums of its inverse matrix
- why geometric multiplicity is bounded by algebraic multiplicity?
- Convergence of a process
- The ratio $\frac{u(z_2)}{u(z_1)}$ for positive harmonic functions is uniformly bounded on compact sets
- Almost sure convergence
- An identity wich applies to all of the natural numbers
- Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
- Is the Odd-4 graph a unit-distance graph without vertex overlap?
- Why are they called “Isothermal” Coordinates?
- The extension $\mathbb{Q}_3 / \mathbb{Q}$ is not algebraic
- Distribution of primes?