33 What is the simplest lower bound on prime counting functions proof wise? 20 Math contest: Find number of roots of $F(x)=\frac{n}{2}$ involving a strange integral. 17 Optimizing response times of an ambulance corp: short-term versus average 15 Why can't $p^p-(p-1)^{p-1}=n^2$ be a square? 15 If $\int_{\mathbb R^2} \frac{\vert f(x)-f(y)\vert}{\vert x-y\vert^2}dxdy<+\infty$ then $f$ is a.e. constant

### Reputation (9,945)

 +40 What is the simplest lower bound on prime counting functions proof wise? +125 Is this function decreasing in $x$? +10 How to generate an ordered list of vertices of a cube from a face and a normal vector +10 An inequality using convex functions: If $\frac{a^2}{1+a^2}+\frac{b^2}{1+b^2}+\frac{c^2}{1+c^2} = 1$ then $abc \le \frac1{2\sqrt 2}$

### Question (1)

 15 Need a *trivial* proof of an “obvious” combinatorial result

### Tags (151)

 60 real-analysis × 21 38 number-theory × 10 60 prime-numbers × 5 36 integration × 5 52 functional-analysis × 11 31 ordinary-differential-equations × 5 48 contest-math × 5 28 optimization × 7 47 calculus × 9 25 combinatorics × 9