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13h
comment Find all natural numbers $a,b,c$ such that $abc+ab+c=a^3$
Is there some more background for this question?
1d
comment Olympiad minimum question, minimal value
You mean A = -3?
1d
comment Olympiad minimum question, minimal value
To minimize the first term, A=B, right?
2d
comment If $a^2+b^2+c^2=1$ then prove the following.
If you were to attempt this problem by Lagrangian optimization, I believe the equations you would get would be equivalent to solving this eigenvalue problem.
2d
revised If $a^2+b^2+c^2=1$ then prove the following.
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2d
answered If $a^2+b^2+c^2=1$ then prove the following.
2d
comment If $a^2+b^2+c^2=1$ then prove the following.
Do you know any linear algebra or calculus?
2d
answered Sum of $1/n+1/(n-2) + 1/(n-4) + \cdots $
Jan
23
comment Proving that $x^5 = x \pmod{10}$ for every integer $x$.
As @Arthur said, you can brute force this very easily. Even more easy if you have access to a computer: repl.it/8mu
Jan
23
revised Graph with fixed amount of spanning trees
adding a picture
Jan
23
answered Graph with fixed amount of spanning trees
Jan
21
awarded  Yearling
Jan
21
revised Why can a circle be described by an equation but not by a function?
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Jan
21
answered Why can a circle be described by an equation but not by a function?
Jan
21
comment How do I show that $\inf\limits_{\det(X)\neq0}\|X^{-1}AX\|^{2}_{F}=\sum\limits_{\lambda\in{\Lambda}}|\lambda|^{2}$?
I think you will use density of diagonalizable matrices along with continuity somewhere
Jan
21
comment How do I show that $\inf\limits_{\det(X)\neq0}\|X^{-1}AX\|^{2}_{F}=\sum\limits_{\lambda\in{\Lambda}}|\lambda|^{2}$?
Maybe you could use $tr(M^T M)$ instead of $||M||_F^2$. It would prove the second part of your question. I'm still not sure about the first part.
Jan
21
comment With $m>n$ , In how many ways $m$ men and $n$ women can seat in row for a photograph so that no two women are adjacent?
Oh thanks. For some reason I just assumed $P^n_k = {n\choose k}$ I'm not familiar with that notation.
Jan
21
comment With $m>n$ , In how many ways $m$ men and $n$ women can seat in row for a photograph so that no two women are adjacent?
What about the permutations of women? For each gender assignment ($m+1 \choose n$ of them) to the chairs, we have $n! m!$ ways of filling the chairs.
Jan
21
revised Use Dominated convergence theorem to show that $f(x):=\sum_{k=1}^{\infty}\frac{\cos(kx)}{k^3}$ is differentiable
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Jan
21
answered Use Dominated convergence theorem to show that $f(x):=\sum_{k=1}^{\infty}\frac{\cos(kx)}{k^3}$ is differentiable