Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10224081 | Journal of Number Theory | 2018 | 7 Pages |
Abstract
For positive integers k and n with k⩽nâ1, let Pn,k(x) denote the polynomial âj=0k(nj)xj, where (nj)=n!j!(nâj)!. In 2011, Khanduja, Khassa and Laishram proved the irreducibility of Pn,k(x) over the field Q of rational numbers for those n,k for which 2â¤2kâ¤n<(k+1)3. In this paper, we extend the above result and prove that if 2â¤2kâ¤n<(k+1)e+1 for some positive integer e and the smallest prime factor of k is greater than e, then there exists an explicitly constructible constant Ce depending only on e such that the polynomial Pn,k(x) is irreducible over Q for kâ¥Ce.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Anuj Jakhar, Neeraj Sangwan,