function sug

### Questions (173)

 26 Show that neither $\frac{p^p-1}{p-1}$ nor $\frac{p^p+1}{p+1}$ can be a prime power 19 How to prove $\sum_{k=1}^{p-1}\frac{2^k}{k^2}\equiv-\frac{(2^{p-1}-1)^2}{p^2}\pmod p$ 17 show this inequality $ab+bc+ac+\sin{(a-1)}+\sin{(b-1)}+\sin{(c-1)}\ge 3$ 16 How prove this Lower bound with $\sum_{i=1}^{n}\prod_{j=1}^{i}a_{j}$ 16 How to find this minimum of the value

### Reputation (333)

 +75 Solve the functional equation $f(xf(y)+yf(x))=yf(x)+xf(y)$ +5 show this inequality with $xy+yz+zx=3$ +20 Solve this equation $\cos{\left(\frac{\pi}{3}-\frac{\pi}{3r}\right)}=\sqrt{\frac{11}{r^2}-2}$ +5 show this $\sum_{cyc}\frac{x}{x^2-x+1}\le\frac{8}{3}$

 2 Calculating general term formula of $a_n$ 0 How find the value of $\sum_{k=0}^{11}(a_{k}\cdot a_{k+1})$

### Tags (85)

 2 sequences-and-series × 11 0 trigonometry × 8 0 inequality × 72 0 elementary-number-theory × 8 0 number-theory × 48 0 a.m.-g.m.-inequality × 7 0 contest-math × 16 0 substitution × 7 0 diophantine-equations × 10 0 cauchy-schwarz-inequality × 5

### Accounts (3)

 MathOverflow 416 rep 211 Mathematics 333 rep 1440 Theoretical Computer Science 101 rep

 +50 Solve the functional equation $f(xf(y)+yf(x))=yf(x)+xf(y)$