Question

If $\frac 1{a+b+c}= \frac 1a+ \frac 1b+ \frac 1c$, then show for odd $n$, $ \frac 1{a^n+b^n+c^n}= \frac 1{a^n}+ \frac 1{b^n}+ \frac 1{c^n}$

score 226 · Answer 1 · 2018-06-02 03:47:19

If $\frac 1{a+b+c}= \frac 1a+ \frac 1b+ \frac 1c$, then show for odd $n$, $ \frac 1{a^n+b^n+c^n}= \frac 1{a^n}+ \frac 1{b^n}+ \frac 1{c^n}$

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List Question

If $\frac 1{a+b+c}= \frac 1a+ \frac 1b+ \frac 1c$, then show for odd $n$, $ \frac 1{a^n+b^n+c^n}= \frac 1{a^n}+ \frac 1{b^n}+ \frac 1{c^n}$

Properties of Matrix Polynomials

Solving the polynomial that doesn't have all the degrees up to the highest one

Nonzero subdeterminants conjecture: has anybody seen this anywhere?

Calculate the $Ker(L_1)$

Construct S polynomial using GAP.

Trouble understanding polynomial GCD

How did root of the equation $x= \sqrt{(2-x)(3-x)} + \sqrt{(3-x)(5-x)} + \sqrt{(2-x)(5-x)}$ vanish while solving?

Ring and field of polynomials

Distinction between $\mathbb{K}(\alpha)$ and $\mathbb{K}[\alpha]$

Prove $\sec^2\frac{\pi}{7}+\sec^2\frac{2\pi}{7}+\sec^2\frac{3\pi}{7}=24$ using the roots of a polynomial

Decomposition of polynomial into polynomials with non-negative coefficients

Multivariate polynomials with infinite number of zeros

Weak Nullstellensatz in practice

Is $\sqrt[n]{x} = 0$ an algebraic equation?

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