106 Can an irrational number raised to an irrational power be rational? 75 How do you describe your mathematical research in layman's terms? 60 Is it morally right and pedagogically right to google answers to homework? 59 Is the ratio of the side and at least one diagonal of a rhombus always irrational? 47 Prove that if two miles are run in 7:59 then one mile MUST be run under 4:00.

### Reputation (107,512)

 +10 Can an irrational number raised to an irrational power be rational? +10 Solving $x^5+px^2y^3+p^2y^5 = 0$ where $p$ is prime and $x,y \in \mathbb{Z}$ +10 Is there an elegant bijective proof of $\binom{15}{5}=\binom{14}{6}$? +10 Solution to a Pell's equation $X^2-1801Y^2=1$

### Questions (37)

 40 Possible distinct positive real $x,y,z \neq 1$ with $x^{(y^z)} = y^{(z^x)} = z^{(x^y)}$ in cyclic permutation? 18 Any more cyclic quintics? 18 Geometry of nose in and nose out parking in parking lots 15 reference for linear algebra books that teach reverse Hermite method for symmetric matrices 13 primes represented integrally by a homogeneous cubic form

### Tags (537)

 2k number-theory × 749 503 matrices × 242 1k elementary-number-theory × 550 445 calculus × 153 909 diophantine-equations × 358 423 algebra-precalculus × 189 830 linear-algebra × 466 410 sequences-and-series × 136 609 prime-numbers × 171 393 geometry × 168