Counting the Unit Solutions of Certain Quartic Diagonal Congruence Modulo

\nGiven a positive integer n and the residue class ring ℤn∶=ℤ/nℤ, we set ℤn× to be the group of units in ℤn, i.e., ℤn×∶={x∈ℤn:gcdx,n=1}. Let Nm(n) be the number of solutions of x14+⋯+xm4≡0 (mod n) with x1,⋯,xm∈ℤn×. In this note, we determine an explicit expression of Nm(n). This extends the results of Sun and Yang in 2014. \n

Publication Details

Journal
Springer Link (Chiba Institute of Technology)
Published
2024-11-20
DOI
https://doi.org/10.1051/wujns/2024295391/pdf
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

Counting the Unit Solutions of Certain Quartic Diagonal Congruence Modulo

Springer Link (Chiba Institute of Technology)
Analytic Number Theory Research
article

Counting the Unit Solutions of Certain Quartic Diagonal Congruence Modulo

article en

Abstract

\nGiven a positive integer n and the residue class ring ℤn∶=ℤ/nℤ, we set ℤn× to be the group of units in ℤn, i.e., ℤn×∶={x∈ℤn:gcdx,n=1}. Let Nm(n) be the number of solutions of x14+⋯+xm4≡0 (mod n) with x1,⋯,xm∈ℤn×. In this note, we determine an explicit expression of Nm(n). This extends the results of Sun and Yang in 2014. \n

Springer Link (Chiba Institute of Technology)
National Natural Science Foundation of China, Natural Science Foundation of Henan Province
Openalex Percentile: Top 49%
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Counting the Unit Solutions of Certain Quartic Diagonal Congruence Modulo · Springer Link (Chiba Institute of Technology) (2024) | TGRS Research Map | TGRS