| Title |
Irreducibility of a polynomial shifted by a power of another polynomial |
| Authors |
Dubickas, Artūras |
| DOI |
10.1155/2020/8869499 |
| Full Text |
|
| Is Part of |
Journal of mathematics.. London : Hindawi Ltd. 2020, vol. 2020, art. no. 8869499, p. [1-4].. ISSN 2314-4629. eISSN 2314-4785 |
| Keywords [eng] |
Irreducible polynomial ; Hilbert's irreducibility theorem ; Capelli's theorem |
| Abstract [eng] |
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]. |
| Published |
London : Hindawi Ltd |
| Type |
Journal article |
| Language |
English |
| Publication date |
2020 |
| CC license |
|
