## Cai, Tianxin

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 Author ID: cai.tianxin Published as: Cai, Tianxin; Cai, Tian Xin; Cai, Tian-Xin External Links: MGP
 Documents Indexed: 82 Publications since 1984, including 3 Books Co-Authors: 21 Co-Authors with 51 Joint Publications 546 Co-Co-Authors
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### Co-Authors

 25 single-authored 14 Shen, Zhongyan 11 Zhang, Yong 8 Zhou, Xia 4 Chen, Deyi 3 Jia, Lirui 3 Xia, Binzhou 3 Yang, Peng 3 Zhong, Hao 2 Bradley, David M. 2 Cao, Jian 2 Fu, Xudan 2 García-Pulgarín, Gilberto 2 Hu, Mengjun 2 Wang, Liuquan 1 Cai, Liping 1 Chern, Shane 1 Chong, C. S. 1 Chua, T. J. 1 Gao, Kaizhou 1 Granville, Andrew James 1 Huang, Jie (Jenny) 1 Jiao, Rongzhen 1 Pan, Quanke 1 Shane, Chern 1 Suganthan, Ponnuthurai Nagaratnam 1 Wang, Feifeng 1 Zhai, Wenguang
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### Serials

 7 Advances in Mathematics 6 Acta Arithmetica 5 Journal of Number Theory 5 International Journal of Number Theory 4 Northeastern Mathematical Journal 3 Rocky Mountain Journal of Mathematics 3 Publicationes Mathematicae 3 Acta Mathematica Sinica. Chinese Series 3 Scientia Sinica. Mathematica 2 Mathematics of Computation 2 Biometrics 2 The Fibonacci Quarterly 2 Proceedings of the American Mathematical Society 2 Journal of Shandong University. Natural Science Edition 2 Journal of Hangzhou University. Natural Science Edition 2 Acta Mathematica Sinica. New Series 2 Acta Mathematica Sinica. English Series 2 JP Journal of Algebra, Number Theory and Applications 1 Bulletin of the Australian Mathematical Society 1 Periodica Mathematica Hungarica 1 Biometrika 1 Czechoslovak Mathematical Journal 1 Functiones et Approximatio. Commentarii Mathematici 1 Information Sciences 1 Journal of the American Statistical Association 1 Mathematica Slovaca 1 Revista Colombiana de Matemáticas 1 Kexue Tongbao 1 Chinese Science Bulletin 1 The Electronic Journal of Combinatorics 1 Journal of Difference Equations and Applications 1 Taiwanese Journal of Mathematics 1 Integers 1 Journal of Zhejiang University. Science A
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### Fields

 74 Number theory (11-XX) 8 Combinatorics (05-XX) 5 Statistics (62-XX) 3 Special functions (33-XX) 2 Algebraic geometry (14-XX) 2 Difference and functional equations (39-XX) 2 Mathematics education (97-XX) 1 Functions of a complex variable (30-XX) 1 Convex and discrete geometry (52-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

36 Publications have been cited 200 times in 87 Documents Cited by Year
Semiparametric regression analysis for clustered failure time data. Zbl 1028.62025
Cai, T.; Wei, L. J.; Wilcox, M.
2000
Regularized estimation for the accelerated failure time model. Zbl 1274.62736
Cai, T.; Huang, J.; Tian, L.
2009
Semiparametric mixed-effects models for clustered failure time data. Zbl 1073.62569
Cai, T.; Cheng, S. C.; Wei, L. J.
2002
Some identities for multiple zeta values. Zbl 1229.11119
Shen, Zhongyan; Cai, Tianxin
2012
A generalization of a curious congruence on harmonic sums. Zbl 1115.11006
Zhou, Xia; Cai, Tianxin
2007
Signed $$q$$-analogs of Tornheim’s double series. Zbl 1204.11150
Zhou, Xia; Cai, Tianxin; Bradley, David M.
2008
On the residues of binomial coefficients and their products modulo prime powers. Zbl 1026.11005
Cai, Tianxin; Granville, Andrew
2002
Bernoulli numbers and congruences for harmonic sums. Zbl 1213.11008
Xia, Binzhou; Cai, Tianxin
2010
On products of consecutive arithmetic progressions. Zbl 1394.11027
Zhang, Yong; Cai, Tianxin
2015
On the Diophantine equation $$f(x)f(y)=f(z^2)$$. Zbl 1291.11066
Zhang, Yong; Cai, Tianxin
2013
A curious congruence modulo prime powers. Zbl 1351.11004
Wang, Liuquan; Cai, Tianxin
2014
Pareto-based grouping discrete harmony search algorithm for multi-objective flexible job shop scheduling. Zbl 1355.90024
Gao, K. Z.; Suganthan, P. N.; Pan, Q. K.; Chua, T. J.; Cai, T. X.; Chong, C. S.
2014
Perfect numbers and Fibonacci primes. I. Zbl 1342.11020
Cai, Tianxin; Chen, Deyi; Zhang, Yong
2015
On 2-Niven numbers and 3-Niven numbers. Zbl 0854.11008
Cai, Tianxin
1996
$$N$$-tuples of positive integers with the same sum and the same product. Zbl 1275.11058
Zhang, Yong; Cai, Tianxin
2013
Identifying subjects who benefit from additional information for better prediction of the outcome variables. Zbl 1172.62063
Tian, L.; Cai, T.; Wei, L. J.
2009
$$n$$-tuples of positive integers with the same second elementary symmetric function value and the same product. Zbl 1285.11059
Zhang, Yong; Cai, Tianxin
2012
A note on the Diophantine equation $$f(x) f(y) = f(z^2)$$. Zbl 1374.11050
Zhang, Yong; Cai, Tianxin
2015
On the diophantine equation $$xy+yz+zx=m$$. Zbl 0864.11015
Cai, Tianxin
1994
A congruence involving the quotients of Euler and its applications. I. Zbl 1008.11001
Cai, Tianxin
2002
Congruences for alternating triple harmonic sums. Zbl 1274.11003
Shen, Zhongyan; Cai, Tianxin
2012
Some identities for alternating multiple zeta values. Zbl 1299.11065
Shen, Zhongyan; Cai, Tianxin
2013
A congruence involving harmonic sums modulo $$p^\alpha q^\beta$$. Zbl 1428.11006
Cai, Tianxin; Shen, Zhongyan; Jia, Lirui
2017
Primes representable by polynomials and the lower bound of the least primes in arithmetic progressions. Zbl 0719.11058
Cai, Tianxin
1990
Rational points on three superelliptic curves. Zbl 1271.11035
Shen, Zhongyan; Cai, Tianxin
2012
A generalization of Lucas’ congruence for $$q$$-binomial coefficients. Zbl 0981.11002
Cai, Tianxin
2001
Two Wolstenholme’s type theorems on $$q$$-binomial coefficients. Zbl 1046.11002
Cai, Tianxin; García-Pulgarín, Gilberto
2001
A new variant of the Hilbert-Waring problem. Zbl 1284.11127
Cai, Tianxin; Chen, Deyi
2013
Depth reduction of a class of Witten zeta functions. Zbl 1235.11083
Zhou, Xia; Bradley, David M.; Cai, Tianxin
2009
On the heights of happy numbers. Zbl 1253.11009
Cai, Tianxin; Zhou, Xia
2008
Mean value estimates for a class of arithmetic function. I. Zbl 0733.11032
Cai, Tianxin
1984
A congruence involving the quotients of Euler and its applications. II. Zbl 1135.11002
Cai, Tianxin; Fu, X. D.; Zhou, X.
2007
The decomposition of triangular numbers. Zbl 1279.11029
Chen, Deyi; Cai, Tianxin
2013
On the sign changes in a weighted divisor problem. Zbl 1428.11172
Jia, Lirui; Cai, Tianxin; Zhai, Wenguang
2017
On $$e$$-power $$b$$-happy numbers. Zbl 1248.11006
Zhou, Xia; Cai, Tianxin
2009
On the Lucas property of linear recurrent sequences. Zbl 1428.11036
Zhong, Hao; Cai, Tianxin
2017
A congruence involving harmonic sums modulo $$p^\alpha q^\beta$$. Zbl 1428.11006
Cai, Tianxin; Shen, Zhongyan; Jia, Lirui
2017
On the sign changes in a weighted divisor problem. Zbl 1428.11172
Jia, Lirui; Cai, Tianxin; Zhai, Wenguang
2017
On the Lucas property of linear recurrent sequences. Zbl 1428.11036
Zhong, Hao; Cai, Tianxin
2017
On products of consecutive arithmetic progressions. Zbl 1394.11027
Zhang, Yong; Cai, Tianxin
2015
Perfect numbers and Fibonacci primes. I. Zbl 1342.11020
Cai, Tianxin; Chen, Deyi; Zhang, Yong
2015
A note on the Diophantine equation $$f(x) f(y) = f(z^2)$$. Zbl 1374.11050
Zhang, Yong; Cai, Tianxin
2015
A curious congruence modulo prime powers. Zbl 1351.11004
Wang, Liuquan; Cai, Tianxin
2014
Pareto-based grouping discrete harmony search algorithm for multi-objective flexible job shop scheduling. Zbl 1355.90024
Gao, K. Z.; Suganthan, P. N.; Pan, Q. K.; Chua, T. J.; Cai, T. X.; Chong, C. S.
2014
On the Diophantine equation $$f(x)f(y)=f(z^2)$$. Zbl 1291.11066
Zhang, Yong; Cai, Tianxin
2013
$$N$$-tuples of positive integers with the same sum and the same product. Zbl 1275.11058
Zhang, Yong; Cai, Tianxin
2013
Some identities for alternating multiple zeta values. Zbl 1299.11065
Shen, Zhongyan; Cai, Tianxin
2013
A new variant of the Hilbert-Waring problem. Zbl 1284.11127
Cai, Tianxin; Chen, Deyi
2013
The decomposition of triangular numbers. Zbl 1279.11029
Chen, Deyi; Cai, Tianxin
2013
Some identities for multiple zeta values. Zbl 1229.11119
Shen, Zhongyan; Cai, Tianxin
2012
$$n$$-tuples of positive integers with the same second elementary symmetric function value and the same product. Zbl 1285.11059
Zhang, Yong; Cai, Tianxin
2012
Congruences for alternating triple harmonic sums. Zbl 1274.11003
Shen, Zhongyan; Cai, Tianxin
2012
Rational points on three superelliptic curves. Zbl 1271.11035
Shen, Zhongyan; Cai, Tianxin
2012
Bernoulli numbers and congruences for harmonic sums. Zbl 1213.11008
Xia, Binzhou; Cai, Tianxin
2010
Regularized estimation for the accelerated failure time model. Zbl 1274.62736
Cai, T.; Huang, J.; Tian, L.
2009
Identifying subjects who benefit from additional information for better prediction of the outcome variables. Zbl 1172.62063
Tian, L.; Cai, T.; Wei, L. J.
2009
Depth reduction of a class of Witten zeta functions. Zbl 1235.11083
Zhou, Xia; Bradley, David M.; Cai, Tianxin
2009
On $$e$$-power $$b$$-happy numbers. Zbl 1248.11006
Zhou, Xia; Cai, Tianxin
2009
Signed $$q$$-analogs of Tornheim’s double series. Zbl 1204.11150
Zhou, Xia; Cai, Tianxin; Bradley, David M.
2008
On the heights of happy numbers. Zbl 1253.11009
Cai, Tianxin; Zhou, Xia
2008
A generalization of a curious congruence on harmonic sums. Zbl 1115.11006
Zhou, Xia; Cai, Tianxin
2007
A congruence involving the quotients of Euler and its applications. II. Zbl 1135.11002
Cai, Tianxin; Fu, X. D.; Zhou, X.
2007
Semiparametric mixed-effects models for clustered failure time data. Zbl 1073.62569
Cai, T.; Cheng, S. C.; Wei, L. J.
2002
On the residues of binomial coefficients and their products modulo prime powers. Zbl 1026.11005
Cai, Tianxin; Granville, Andrew
2002
A congruence involving the quotients of Euler and its applications. I. Zbl 1008.11001
Cai, Tianxin
2002
A generalization of Lucas’ congruence for $$q$$-binomial coefficients. Zbl 0981.11002
Cai, Tianxin
2001
Two Wolstenholme’s type theorems on $$q$$-binomial coefficients. Zbl 1046.11002
Cai, Tianxin; García-Pulgarín, Gilberto
2001
Semiparametric regression analysis for clustered failure time data. Zbl 1028.62025
Cai, T.; Wei, L. J.; Wilcox, M.
2000
On 2-Niven numbers and 3-Niven numbers. Zbl 0854.11008
Cai, Tianxin
1996
On the diophantine equation $$xy+yz+zx=m$$. Zbl 0864.11015
Cai, Tianxin
1994
Primes representable by polynomials and the lower bound of the least primes in arithmetic progressions. Zbl 0719.11058
Cai, Tianxin
1990
Mean value estimates for a class of arithmetic function. I. Zbl 0733.11032
Cai, Tianxin
1984
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### Cited by 101 Authors

 13 Cai, Tianxin 9 Zhang, Yong 7 Shen, Zhongyan 6 Meštrović, Romeo 5 Zhao, Jianqiang 4 Wang, Liuquan 3 Jia, Lirui 3 Nakamura, Takashi 3 Niţică, Viorel 3 Ulas, Maciej 2 Cao, Huiqin 2 Chen, Kwang-Wu 2 Chu, Hùng Việt 2 Chung, Chan-Liang 2 Dilcher, Karl 2 Ding, Shifeng 2 Eie, Minking 2 Kim, Daeyeoul 2 Komori, Yasushi 2 Li, Zhong-Hua 2 Liu, Weijun 2 Machide, Tomoya 2 Matsumoto, Kohji 2 Pan, Hao 2 Seki, Shin-ichiro 2 Tasaka, Koji 2 Tsumura, Hirofumi 2 Xu, Ce 1 Ayad, Mohamed 1 Bailey, David Harold 1 Bibby, Sean 1 Borwein, Jonathan Michael 1 Cha, Byungchul 1 Chan, Ada 1 Chen, Deyi 1 Chen, Shaoshi 1 Chen, Zhuoyu 1 Claman, Adam 1 Coppenbarger, Matthew E. 1 Cosgrave, John B. 1 Das, Pranabesh 1 De Koninck, Jean-Marie 1 Doyon, Nicolas 1 Elsner, Carsten 1 Feng, Lihua 1 Genčev, Marian 1 Gorodetsky, Ofir 1 Guo, Li 1 Harrington, Joshua 1 He, Hua 1 Hessami Pilehrood, Khodabakhsh 1 Hessami Pilehrood, Tatiana 1 Hoffman, Michael E. 1 Hong, Rachel 1 Jeong, Kyung Ho 1 Jiang, Xing-Wang 1 Jiao, Rongzhen 1 Kadota, Shin-Ya 1 Kátai, Imre 1 Kihel, Omar 1 Kim, Soeun 1 Laishram, Shanta 1 Lei, Peng 1 Li, Yan 1 Lim, Donghyeok 1 Lin, XianZu 1 Liu, Jianxin 1 Liu, Ziyu 1 Louboutin, Stéphane R. 1 Ma, Lianrong 1 Maldonado, Barbara 1 Matiyasevich, Yuriĭ Vladimirovich 1 Mattarei, Sandro 1 McCoy, Megan 1 Murahara, Hideki 1 Newman, Michael Frederick 1 Okamoto, Takuya 1 Ong, Yaolin 1 Onozuka, Tomokazu 1 Palma, Ann 1 Qu, Jerry 1 Rahmani, Mourad 1 Saradha, N. 1 Singer, Michael F. 1 So, Jisuk 1 Spilker, Jürgen 1 Sun, Zhi-Wei 1 Tauraso, Roberto 1 Tengely, Szabolcs 1 Teo, Lee-Peng 1 Thielen, Kevin 1 Vyncke, Pieter 1 Wong, Tony W. H. 1 Xia, Binzhou 1 Yamamoto, Shuji 1 Yang, Peng 1 Yi, Hongkwon 1 Zargar, Arman Shamsi 1 Zelinsky, Joshua 1 Zhai, Wenguang ...and 1 more Authors
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### Cited in 42 Serials

 19 Journal of Number Theory 13 International Journal of Number Theory 4 Journal of Integer Sequences 3 Periodica Mathematica Hungarica 3 Tokyo Journal of Mathematics 3 Integers 2 American Mathematical Monthly 2 Mathematics of Computation 2 Acta Arithmetica 2 Colloquium Mathematicum 2 Functiones et Approximatio. Commentarii Mathematici 2 The Ramanujan Journal 1 Bulletin of the Australian Mathematical Society 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 Archiv der Mathematik 1 Czechoslovak Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Algebra 1 Journal of the Mathematical Society of Japan 1 Mathematica Slovaca 1 Mathematika 1 Osaka Journal of Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Advances in Applied Mathematics 1 Bulletin of the Korean Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematica Hungarica 1 Forum Mathematicum 1 Elemente der Mathematik 1 Acta Mathematica Sinica. New Series 1 Chinese Science Bulletin 1 Journal de Théorie des Nombres de Bordeaux 1 The Electronic Journal of Combinatorics 1 Acta Mathematica et Informatica Universitatis Ostraviensis 1 Journal of Applied Mathematics 1 Mediterranean Journal of Mathematics 1 Advances in Difference Equations 1 Journal of Applied Mathematics & Informatics 1 Journal of Mathematics 1 ISRN Combinatorics 1 Algebraic Combinatorics
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### Cited in 14 Fields

 84 Number theory (11-XX) 14 Combinatorics (05-XX) 6 Special functions (33-XX) 3 Sequences, series, summability (40-XX) 2 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Mathematics education (97-XX)