# Alex

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bio website location age 19 member for 1 year, 11 months seen Mar 13 at 9:04 profile views 23

Senior in high school. I love math and am on my school's math team. I'd love to at least minor in math in college.

# 5 Questions

 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 $<4$.

# 304 Reputation

 +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

# 14 Tags

 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

# 1 Account

 Mathematics 304 rep 111

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