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Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{T}(y)\ll \frac{y}{(\log{y})^2}.$$

Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{T}(y)\ll \frac{y}{(\log{y})^2}.$$

Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$. We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{T}(y)\ll \frac{y}{(\log{y})^2}.$$

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Hhhhhhhhhhh
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Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{T}(x)\ll \frac{x}{(\log{x})^2}.$$$$\#\mathcal{T}(y)\ll \frac{y}{(\log{y})^2}.$$

Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{T}(x)\ll \frac{x}{(\log{x})^2}.$$

Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{T}(y)\ll \frac{y}{(\log{y})^2}.$$

deleted 20 characters in body; edited title
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Hhhhhhhhhhh
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Estimating the size of set of primes $p$ for which the polynomial is not bijective in $\mathbb{F}_p[X]$

Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{P}\setminus\mathcal{T}(x)\ll \frac{x}{(\log{x})^2}.$$$$\#\mathcal{T}(x)\ll \frac{x}{(\log{x})^2}.$$

Estimating the size of set of primes $p$ for which the polynomial is not bijective in $\mathbb{F}_p[X]$

Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{P}\setminus\mathcal{T}(x)\ll \frac{x}{(\log{x})^2}.$$

Estimating the size of set of primes $p$ for which the polynomial is bijective in $\mathbb{F}_p[X]$

Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{T}(x)\ll \frac{x}{(\log{x})^2}.$$

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Hhhhhhhhhhh
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