Alex
Reputation
304
Top tag
Next privilege 500 Rep.
Access review queues
1 11
Impact
~3k people reached

• 0 posts edited

### Questions (5)

 18 Find all roots of $\,(x + 1)(x + 2)(x + 3)^2(x + 4)(x + 5) = 360$ 16 Prove that for any nonnegative integer n the number $5^{5^{n+1}} + 5^{5 ^n} + 1$ is not prime 13 Find the number of pairs $(m, n)$ of positive integers such that $\frac{ m}{n+1} < \sqrt{2} < \frac{m+1}{n}$ 5 Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$ 3 A polynomial has only real roots and all coefficients $\pm 1$. Prove the degree $<4$.

### Reputation (304)

 +10 Prove that for any nonnegative integer n the number $5^{5^{n+1}} + 5^{5 ^n} + 1$ is not prime +10 Find the number of pairs $(m, n)$ of positive integers such that $\frac{ m}{n+1} < \sqrt{2} < \frac{m+1}{n}$ +15 Find all roots of $\,(x + 1)(x + 2)(x + 3)^2(x + 4)(x + 5) = 360$ +5 Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$

 2 Moving on the surface of a cube

### Tags (14)

 2 combinatorics × 2 0 polynomials 2 3d 0 prime-numbers 0 roots × 2 0 problem-solving 0 inequality × 2 0 proof-writing 0 number-theory × 2 0 complex-numbers

### Account (1)

 Mathematics 304 rep 111