MathOverflow

One of the most well known exponential diophantine equations is $(x^n-1)/(x-1)=y^p$, where $x,n,y,p$ are positive Integers with $n>2$, $x>1$, and $p$ prime. Some solutions are obtained with $x=3, n=5$, $x=7,n=4$, and also with $x=18,n=3$. Are...

This question concerns the closure of $\{0\}$ under multiplication, negation, and exponentiation by primes.
Let $S \subseteq \mathbb{R}$ be the smallest set satisfying the following closure properties:
$0 \in S$;

I've heard it said many times times that $\boldsymbol{\Pi}^{1}_{n}$-determinacy implies $\boldsymbol{\Sigma}^{1}_{n+1}$-Lebesgue measurability (hence for instance $n$ many Woodin cardinals with a measurable cardinal above gives $\boldsymbol\Pi^{1}_{n...

Let $u$ be a solution to the heat equation $u_t = \Delta u$ in the unit cylinder $B_1\times(-1,0) \subset \mathbb R^{n+1}$.
Then, it is well known (see for instance Chapter 2 in "Watson - Introduction to heat potential theory") that one can write$$u(0,0) = \int_{B_1\times\{0\}}u(x,-1)\mathrm{d}\omega_i(x) + \int_0^1\int_{\partial B_1}u(x,t)\mathrm{d}\omega_l(x,t),$$and that...