Nonexistence conditions of a solution
for the congruence
Authors:
Hiroshi Sekigawa and Kenji Koyama
Journal:
Math. Comp. 68 (1999), 1283-1297
MSC (1991):
Primary 11D79; Secondary 11P05
DOI:
https://doi.org/10.1090/S0025-5718-99-01067-4
Published electronically:
February 24, 1999
MathSciNet review:
1627821
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We obtain nonexistence conditions of a solution for of the congruence , where
,
and
are integers, and
is a prime power. We give nonexistence conditions of the form
for
,
,
,
,
, and of the form
for
,
,
,
. Furthermore, we complete some tables concerned with Waring's problem in
-adic fields that were computed by Hardy and Littlewood.
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, Math. Comp. 66 (1997), 841-851. MR 97m:11041
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Additional Information
Hiroshi Sekigawa
Affiliation:
NTT Communication Science Laboratories, 2-4 Hikaridai, Seika-cho, Soraku-gun Kyoto 619-0237 Japan
Email:
sekigawa@cslab.kecl.ntt.co.jp
Kenji Koyama
Affiliation:
NTT Communication Science Laboratories, 2-4 Hikaridai, Seika-cho, Soraku-gun Kyoto 619-0237 Japan
Email:
koyama@cslab.kecl.ntt.co.jp
DOI:
https://doi.org/10.1090/S0025-5718-99-01067-4
Keywords:
Congruences,
Diophantine equations,
solvability,
Waring's problem in $p$-adic fields,
computer search
Received by editor(s):
December 1, 1997
Published electronically:
February 24, 1999
Article copyright:
© Copyright 1999
American Mathematical Society