Abstract
We show that an element f in the ring Z[[x]] of formal power series over the integers is a sum of two irreducible elements in Z[[x]] if and only if the constant term of f is of the form ±pk±ql or of the form ±pk, where p,q are prime numbers and k,l are positive integers. Moreover, if f0 is of such form, then there exist 2ℵ0 pairwise coprime elements g∈Z[[x]] such that both g and g+f are irreducible.
Original language | English |
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Pages (from-to) | 453-461 |
Number of pages | 9 |
Journal | Journal of Number Theory |
Volume | 213 |
DOIs | |
State | Published - Aug 2020 |
Bibliographical note
Publisher Copyright:© 2020 Elsevier Inc.
Keywords
- Goldbach's conjecture
- Rings of formal power series
- Twin-prime conjecture