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 Solve the functional equation $f(xf(y)+yf(x))=yf(x)+xf(y)$ 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 $\sum_{i=1}^{n}\prod_{j=1}^{i}a_{j}$

### Reputation (295)

 +5 How prove this identity $\sum\limits_{i=1}^{n}\sum\limits_{j=1}^{n}\min{\{i,j\}}(a_{i}-a_{i+1})(b_{j}-b_{j+1})=\sum\limits_{i=1}^{n}a_{i}b_{i}$? +85 Solve the functional equation $f(xf(y)+yf(x))=yf(x)+xf(y)$ +5 show this inequality with $xy+yz+zx=3$ +5 Solve this equation $\cos{\left(\frac{\pi}{3}-\frac{\pi}{3r}\right)}=\sqrt{\frac{11}{r^2}-2}$

 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 (84)

 2 sequences-and-series × 11 0 trigonometry × 9 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 summation × 6