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Francesco Polizzi
Francesco Polizzi
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Some What are conditions such that the polynomial $x^2+1$ dividedivides $p(y)+q(z)+ax+b=F(x,y\, y, \,z)$?

I came across the following problem:

What are conditions such that the polynomial $x^2+1$ divides $p(y)+q(z)+ax+b=F(x,\,y,\,z)$,?

How one can makes some conditions such that the polynomial $x^2+1$ divide $p(y)+q(z)+ax+b=F(x,y,z)$. Here $p$ and $q$ are somealso polynomials and $a$ and, $b$ are real numbers. The main difficulty here is that $F(x,y,z)$$F(x,\, y, \,z)$ has three variables, and the fact the idea of using roots cannot apply here. I am expectedexpecting a relation between $x$ and $y,z$, but I not able to find it.

Some conditions such that the polynomial $x^2+1$ divide $p(y)+q(z)+ax+b=F(x,y,z)$

I came across the following problem:

How one can makes some conditions such that the polynomial $x^2+1$ divide $p(y)+q(z)+ax+b=F(x,y,z)$. Here $p$ and $q$ are some polynomials and $a$ and $b$ are real numbers. The main difficulty here is that $F(x,y,z)$ has three variables and the fact the idea of using roots cannot apply here. I am expected a relation between $x$ and $y,z$, but I not able to find it.

What are conditions such that the polynomial $x^2+1$ divides $p(y)+q(z)+ax+b=F(x,\, y, \,z)$?

I came across the following problem:

What are conditions such that the polynomial $x^2+1$ divides $p(y)+q(z)+ax+b=F(x,\,y,\,z)$,?

Here $p$ and $q$ are also polynomials and $a$, $b$ are real numbers. The main difficulty is that $F(x,\, y, \,z)$ has three variables, and the idea of using roots cannot apply here. I am expecting a relation between $x$ and $y,z$, but I not able to find it.

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Safwane
Safwane
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Some conditions such that the polynomial $x^2+1$ divide $p(y)+q(z)+ax+b=F(x,y,z)$

I came across the following problem:

How one can makes some conditions such that the polynomial $x^2+1$ divide $p(y)+q(z)+ax+b=F(x,y,z)$. Here $p$ and $q$ are some polynomials and $a$ and $b$ are real numbers. The main difficulty here is that $F(x,y,z)$ has three variables and the fact the idea of using roots cannot apply here. I am expected a relation between $x$ and $y,z$, but I not able to find it.