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1d
awarded  Popular Question
1d
comment An exercise regarding polynomials
Unfortunately it is incomplete. $X^{4000}+X^{401}+X^{42}+X^3$ is also a solution for example
1d
comment How prove this inequatity $\frac{x^2}{y}+\frac{y^2}{z}+\frac{z^2}{x}\ge 4+(x-y)^2$
@Sawarnik with the help of PARI-GP on my computer
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comment An exercise regarding polynomials
Hmm. Very nice factorization, but it’s not very helpful here. I find your hint unconvincing.
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revised An exercise regarding polynomials
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answered An exercise regarding polynomials
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answered Automorphism that maps primitive roots of unity.
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answered How prove this $|1+x|^a\ge 1+ax+\dfrac{1}{1000}|x|^a$
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comment How prove this inequatity $\frac{x^2}{y}+\frac{y^2}{z}+\frac{z^2}{x}\ge 4+(x-y)^2$
@CalvinLin The upper bound of $5$ is not that much of a red herring, as when $x=0.54,y=3.16,z=1.35$, the inequality becomes false, but the sum $x+y+z=5.05$ is remarkably near to $5$.
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revised Period of $f(2x+3)+f(2x+7)=2$
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Apr
16
answered Period of $f(2x+3)+f(2x+7)=2$
Apr
15
comment Characteristic vector components expressed as polynomial in $A$ and $\lambda$
There are several candidates for the "polynomial solutions", and you cannot know in advance which is going to be right. Similarly, you cannot know in advance which $|A_k-\lambda I|$ will be nonzero. So there is no unique solution, there is only a finite set of possible solutions. In each special case with specific numerical values you decide which candidates are right by looking whether certain quantities are nonzero. In algebraic geometry language, you need to decompose your algebraic variety into irreducible components.
Apr
14
answered How prove this can choose two postive integer numbers $a_{m},a_{k},$such $\frac{a_{m}+a_{k}}{3a_{p}}\notin N^{+},$
Apr
13
comment Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
@MadHatter Inserted the $\sigma^2$ back in, thanks.
Apr
13
revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
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Apr
13
answered Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
Apr
12
revised Show that $G$ ( subgroup of $\mathrm{GL}(E)$) is finite.
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Apr
12
revised Show that $G$ ( subgroup of $\mathrm{GL}(E)$) is finite.
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Apr
12
answered Show that $G$ ( subgroup of $\mathrm{GL}(E)$) is finite.
Apr
12
revised How prove this can choose two postive integer numbers $a_{m},a_{k},$such $\frac{a_{m}+a_{k}}{3a_{p}}\notin N^{+},$
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