query: Prove that any polynomial with integer coefficients must have a composite number in its image.
positive_passages.docid: 155575
positive_passages.text: Proving a polynomial $f(x)$ composite for infinitely many $x$
negative_passages.docid: 2408
negative_passages.text: Show that a polynomial has at least one positive solution/root.
negative_passages.docid: 103763
negative_passages.text: Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$
negative_passages.docid: 129834
negative_passages.text: Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
negative_passages.docid: 51094
negative_passages.text: Prove that the set of integer coefficients polynomials is countable
negative_passages.docid: 62239
negative_passages.text: For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
negative_passages.docid: 139230
negative_passages.text: Prove that for every positive integer, this polynomial is divisible by 24.
negative_passages.docid: 141184
negative_passages.text: Proof that a degree 4 polynomial has at least two roots
negative_passages.docid: 144592
negative_passages.text: how to prove the existence and uniqueness of the prime factorization of any natural number.
negative_passages.docid: 5802
negative_passages.text: Proving the universal mapping property for polynomial rings
negative_passages.docid: 94209
negative_passages.text: Prove by contradiction that every integer greater than 11 is a sum of two composite numbers
negative_passages.docid: 95594
negative_passages.text: Prove that a polynomial is irreducible or the field contains a $p$th root
negative_passages.docid: 81682
negative_passages.text: Proving the algebraic set corresponding to a polynomial is infinite.
negative_passages.docid: 65757
negative_passages.text: Prove that $n! + k$ is a composite number
negative_passages.docid: 22367
negative_passages.text: How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
negative_passages.docid: 53244
negative_passages.text: Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
negative_passages.docid: 26514
negative_passages.text: Prove that if $n$ is a composite, then $2^n-1$ is composite.