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kodlu
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It is addressed in the The math overflow post thatasks whether the equation $1+z^p+z^q=z^n$ can have no multiple complex roots where $p<q<n$ (On the irreducibility of certain trinomials and quadrinomials).

Q. Let us consider the polynomial $\mathbf{P}(z)=1+z^p+z^q+z^r-z^n$ where $p,q,r$ and $n$ are natural numbers with $1<p<q<r<n$. Has $\mathbf{P}$ any multiple complex root?

It is addressed in the post that the equation $1+z^p+z^q=z^n$ have no multiple complex roots where $p<q<n$ (On the irreducibility of certain trinomials and quadrinomials).

Q. Let us consider the polynomial $\mathbf{P}(z)=1+z^p+z^q+z^r-z^n$ where $p,q,r$ and $n$ are natural numbers with $1<p<q<r<n$. Has $\mathbf{P}$ any multiple complex root?

The math overflow post asks whether the equation $1+z^p+z^q=z^n$ can have multiple complex roots where $p<q<n$ (On the irreducibility of certain trinomials and quadrinomials).

Q. Let us consider the polynomial $\mathbf{P}(z)=1+z^p+z^q+z^r-z^n$ where $p,q,r$ and $n$ are natural numbers with $1<p<q<r<n$. Has $\mathbf{P}$ any multiple complex root?

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GH from MO
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Daniele Tampieri
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Can the equation $1+z^p+z^q+z^r=z^n$ have multiple complex roots z$z$?

It is addressed in the post that the equation $1+z^p+z^q=z^n$ have no multiple complex roots where $p<q<n$ (On the irreducibility of certain trinomials and quadrinomials).

Q. Let us consider the polynomial $\mathbf{P}(z)=1+z^p+z^q+z^r-z^n$ where $p,q,r$ and $n$ are natural numbers with $1<p<q<r<n$. Has \mathbf{P}$\mathbf{P}$ any multiple complex root?

Can the equation $1+z^p+z^q+z^r=z^n$ have multiple complex roots z?

It is addressed in the post that the equation $1+z^p+z^q=z^n$ have no multiple complex roots where $p<q<n$ (On the irreducibility of certain trinomials and quadrinomials).

Q. Let us consider the polynomial $\mathbf{P}(z)=1+z^p+z^q+z^r-z^n$ where $p,q,r$ and $n$ are natural numbers with $1<p<q<r<n$. Has \mathbf{P} any multiple complex root?

Can the equation $1+z^p+z^q+z^r=z^n$ have multiple complex roots $z$?

It is addressed in the post that the equation $1+z^p+z^q=z^n$ have no multiple complex roots where $p<q<n$ (On the irreducibility of certain trinomials and quadrinomials).

Q. Let us consider the polynomial $\mathbf{P}(z)=1+z^p+z^q+z^r-z^n$ where $p,q,r$ and $n$ are natural numbers with $1<p<q<r<n$. Has $\mathbf{P}$ any multiple complex root?

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ABB
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