primitiveroot

### Questions (22)

 13 Choose $3n$ points on a circle, show that there are two diametrically opposite point 9 Write $n^2$ real numbers into $n \times n$ square grid 8 Find the least possible value of $n$ such that there exist $P(x), Q(x) \in \mathbb{Z}[x]$ 6 Show that there are no integers $x, y$ such that $x^{2015} - y^{2016} = 2115$ 5 Partition of $S = \{1,2,\dots, 3n\}$ in to three subsets $A, B, C$ such that $|A| = |B| = |C| = n$

### Reputation (825)

 +10 If $a+b+c+d=4$, then $\sum\frac{1}{a+3}\le \frac{1}{abcd}$ +10 Limit of a finite sum +30 Choose $3n$ points on a circle, show that there are two diametrically opposite point +10 Show that there are no integers $x, y$ such that $x^{2015} - y^{2016} = 2115$

 2 Proof that $x_{n+1} = 1+\frac{2}{x_n}$ is monotonally decreasing for all $n = 2k$ 2 Does the equation $f(x)+g(y)=x^2+xy+y^2$ have solutions in real functions $f$ and $g$? 2 If $a+b+c+d=4$, then $\sum\frac{1}{a+3}\le \frac{1}{abcd}$ 0 What is the limit for the radical $\sqrt{x^2+x+1}-x$?

### Tags (35)

 2 functional-equations × 3 2 symmetric-polynomials 2 algebra-precalculus × 2 0 combinatorics × 8 2 inequality 0 number-theory × 6 2 functional-analysis 0 elementary-number-theory × 5 2 induction 0 integers × 5