|
|||||
|
|
Upper bounds for the prime divisors of Wendt's determinant |
|
| Authors: | Anastasios Simalarides |
| Institution: | T.E.I. of Chalcis, Psahna 34400, Euboea, Greece |
| Abstract: | Let |
| Keywords: | Wendt's determinant Fermat's congruence |
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 | |
| 点击此处可从《Mathematics of Computation》下载免费的PDF全文 | |
be an even integer, 
. The resultant 
of the polynomials 
and 
is known as Wendt's determinant of order 
. We prove that among the prime divisors 
of 
only those which divide 
or 
can be larger than 
, where 
and 
is the 
th Lucas number, except when 
and 
. Using this estimate we derive criteria for the nonsolvability of Fermat's congruence.