299 reputation
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age 19
visits member for 1 year, 10 months
seen Mar 13 at 9:04

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.


Sep
24
awarded  Autobiographer
Dec
25
awarded  Yearling
Sep
18
awarded  Commentator
Sep
18
awarded  Editor
Sep
18
revised A polynomial has only real roots and all coefficients $\pm 1$. Prove the degree $<4$.
added 5 characters in body; edited title
Sep
18
comment A polynomial has only real roots and all coefficients $\pm 1$. Prove the degree $<4$.
Yes allow me to correct that. The source for the problem also made that mistake.
Sep
18
asked A polynomial has only real roots and all coefficients $\pm 1$. Prove the degree $<4$.
Mar
5
awarded  Nice Question
Mar
1
awarded  Teacher
Mar
1
answered Moving on the surface of a cube
Mar
1
comment Moving on the surface of a cube
Excellent, because I posed this question to Brian randomly. My solution goes: $\frac{9!}{(3!)^{3}} - 3(2(\frac{6!}{(2!)^{2}}) + 6(\frac{5!}{(2!)^{2}}) + 6(\frac{4!}{2!}))$
Feb
28
comment Moving on the surface of a cube
What did you get Jorge? By the way, you can only use the 3rd 4th and 5th positions for the third letter. And, this can be done 3 times - for all the combinations of two letter.
Feb
28
awarded  Critic
Feb
28
comment Moving on the surface of a cube
I mean that they are travels where you must go on the inside of the cube, because the question asks for only surface or "outside" travels
Feb
28
comment Moving on the surface of a cube
This is exactly my process and I counted 384 ways. 1680 including inside travels and 1296 on only inside travels. Someone can check
Dec
31
comment Proof of $\log_xy=\frac{\log_zy}{\log_zx}$
Also $\log_{z}x^\log_{x}y = \log_{z}y$ which you can then simplify to $y=y$ (And could someone edit this, because I am not understanding the programming)
Dec
27
awarded  Nice Question
Dec
27
comment Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$
Interestingly enough, because of the symmetry of the roots, setting $x=\frac{1}{y^2}$ and using Vieta's formula on the $y^2$ term yields the same result. I assume that the other answer given also used Chebyshev polynomials of the first kind? I appreciate the explanation on the recursive nature of $cos(n\theta)$
Dec
27
accepted Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$
Dec
26
comment Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$
How is it known that $t^7−21t^5+35t^3−7t$ has roots $tan(r\pi/7)$