In this note, we show that, for any f ∈ Z[x] and any prime number p, there exists g ∈ Z[x] for which the polynomial f(x) − g(x)p is irreducible over Q. For composite p ≥ 2, this assertion is not true in general. However, it holds for any integer p ≥ 2 if f is not of the form ah(x)k, where a ≠ 0 and k ≥ 2 are integers and h ∈ Z[x]
AbstractWe prove that if K is a finite extension of Q, P is the set of prime numbers in Z that remai...
Abstract. In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polyn...
In 1956, Ehrenfeucht proved that a polynomial f <SUB>1</SUB>(x <SUB>1</SUB>) + · + f <SUB>n</SUB> (x...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...
Given an Hilbertian fieldK, a polynomial g(x) ∈ K[x] and an integer n ∈ N, we show that there exist...
AbstractWe characterize the polynomials P(X, Y) that are irreducible over a number field K and such ...
We give a simple argument to show if a = b ∈ Z so that no prime p has the property p2|a or p2|b, th...
Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their ap...
Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their ap...
Any irreducible polynomial f(x) in [special characters omitted][x] such that the set of values f([sp...
ii Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some inte...
In this paper, all irreducible factors of bivariate polynomials of the form f(x) - g(y) over an arbi...
In this paper, all irreducible factors of bivariate polynomials of the form f(x) - g(y) over an arbi...
We explore two specific connections between prime numbers and polynomials. Cohn\u27s C...
AbstractThis work is a continuation and extension of our earlier articles on irreducible polynomials...
AbstractWe prove that if K is a finite extension of Q, P is the set of prime numbers in Z that remai...
Abstract. In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polyn...
In 1956, Ehrenfeucht proved that a polynomial f <SUB>1</SUB>(x <SUB>1</SUB>) + · + f <SUB>n</SUB> (x...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...
Given an Hilbertian fieldK, a polynomial g(x) ∈ K[x] and an integer n ∈ N, we show that there exist...
AbstractWe characterize the polynomials P(X, Y) that are irreducible over a number field K and such ...
We give a simple argument to show if a = b ∈ Z so that no prime p has the property p2|a or p2|b, th...
Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their ap...
Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their ap...
Any irreducible polynomial f(x) in [special characters omitted][x] such that the set of values f([sp...
ii Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some inte...
In this paper, all irreducible factors of bivariate polynomials of the form f(x) - g(y) over an arbi...
In this paper, all irreducible factors of bivariate polynomials of the form f(x) - g(y) over an arbi...
We explore two specific connections between prime numbers and polynomials. Cohn\u27s C...
AbstractThis work is a continuation and extension of our earlier articles on irreducible polynomials...
AbstractWe prove that if K is a finite extension of Q, P is the set of prime numbers in Z that remai...
Abstract. In [3] we showed that a polynomial over a Noetherian ring is divisible by some other polyn...
In 1956, Ehrenfeucht proved that a polynomial f <SUB>1</SUB>(x <SUB>1</SUB>) + · + f <SUB>n</SUB> (x...
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