9 Explain phrase "For each pair of distinct elements" in reference to a graph. 9 Book on Curry-Howard Isomorphisms 8 What is the definition of the density of a graph? 8 Proof that $n^{n} \leq {(n+1)}^{n}$ 8 Computation of a limit involving factorial $\lim_{n \to \infty} \sqrt[n+1] {(n+1)!} - \sqrt[n] {(n)!} = \frac{1}{e}$

### Reputation (9,872)

 -2 A proposed unconditional factor-chain proof for the inequality $I(n) > \frac{3}{2}$, where $q^k n^2$ is an odd perfect number with special prime $q$ +10 Is it possible to improve on these bounds for $\frac{\varphi(n)}{n}$, if $q^k n^2$ is an odd perfect number with special prime $q$? +25 Analytical Geometry Techniques to sketch curves? +15 Combinatorial interpretation of Euclid's form for even perfect numbers

### Questions (438)

 18 When $p$ is an odd prime, is $(p+2)/p$ an outlaw or an index? 17 If $N = q^k n^2$ is an odd perfect number and $n < q^{k+1}$, does it follow that $k > 1$? 11 Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions? 11 Examples of fallacies in arithmetic and/or algebra [closed] 10 How did Descartes come up with the spoof odd perfect number $198585576189$?

### Tags (219)

 94 number-theory × 306 49 inequality × 175 87 elementary-number-theory × 350 48 divisor-sum × 362 83 perfect-numbers × 341 35 calculus × 39 75 reference-request × 89 29 book-recommendation × 24 57 algebra-precalculus × 96 27 conjectures × 139

### Bookmarks (1,026)

 1484 Visually stunning math concepts which are easy to explain 1177 Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio? 826 The staircase paradox, or why $\pi\ne4$ 812 How to study math to really understand it and have a healthy lifestyle with free time? [closed] 783 A proof for $\dim(R[T])=\dim(R)+1$ without prime ideals?