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| Residue Class Ring with Identical Representation Function |
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Citation： |
Shiqiang CHEN.Residue Class Ring with Identical Representation Function[J].Chinese Annals of Mathematics B,2026,(2):413~420 |
| Page view： 86
Net amount： 26 |
Authors： |
Shiqiang CHEN; |
Foundation： |
National Natural Science Foundation of China (No. 12301003); Anhui Provincial Natural Science Foundation (No. 2308085QA02); University Natural Science Research Project of Anhui Province (No. 2022AH050171) |
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| Abstract： |
For an integer m≥2 let Z/mZ be the set of all residue classes mod m. For S?Z/mZ and nˉ∈Z/mZ, RS?(nˉ) is defined as the number of solutions to the equation nˉ=sˉ+s′ with an unordered pair (sˉ,s′)∈S2 and sˉ=s′. In this paper, the author determines the structures of sets A and B such that A∪B=Z/mZ, A∩B=kˉZ and RA?(nˉ)=RB?(nˉ) for all nˉ∈Z/mZ, where k is an integer. |
Keywords： |
Residue class Representation function |
Classification： |
11B13 |
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