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武汉大学学报 英文版 | Wuhan University Journal of Natural Sciences
Wan Fang
CNKI
CSCD
Wuhan University
Latest Article
An Equivalent Form of Strong Lemoine Conjecture and Several Relevant Results
Time:2019-5-20  
ZHANG Shaohua
School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408102, China
Abstract:
In this paper, we consider some problems involving Strong Lemoine Conjecture in additive number theory. Based on Dusart’s inequality and Rosser-Schoenfeld’s inequality, we obtain several new results and give an equivalent form of Strong Lemoine Conjecture.
Key words:Lemoine Conjecture; Dusart’s inequality; Rosser-Schoenfeld’s inequality; Euler totient function; prime- counting function
CLC number: O 156
References:
[1]	Dickson L E. History of the Theory of Numbers[M]. New York: Chelsea, 1952.
[2]	Hardy G H, Littlewood J E. On some problems of “partitio numerorum” III: On the expression of a number as a sum of primes [J]. Acta Math, 1923, (44): 1-70. 
[3]	Chen J R. On the representation of a larger even integer as the sum of a prime and the product of at most two primes [J]. Sci Sinica, 1973, (16): 157-176.
[4]	Tao T. Every odd number greater than 1 is the sum of at most five primes[J]. Math Comp, 2014, 83 (286): 997-1038.
[5]	Helfgott H. The ternary Goldbach conjecture [J]. Gac R Soc Mat Esp, 2013, 16(4): 709-726.
[6]	Zhao L L. On ternary problems in additive prime number theory [J]. J Number Theory, 2017, (178): 179-189.
[7]	Banks W D. Zeta functions and asymptotic additive bases with some unusual sets of primes [J]. Ramanujan J, 2018, 45(1): 57-71.
[8]	Kiltinen J O, Young P B. Goldbach, Lemoine, and a know/don’t know problem [J]. Math Mag, 1985, 58(4): 195-203.
[9]	Sun Z W. On sums of primes and triangular numbers [EB/OL]. [2018-04-17]. https://arxiv.org/abs/0803.3737.
[10]	Dusart P. Estimates of some functions over primes without R.H. [EB/OL]. [2018-04-17]. https://arxiv.org/abs/1002. 0442.
[11]	Rosser J B, Schoenfeld L. Approximate formulas for some functions of prime numbers [J]. Illinois J Math, 1962, (1): 64-94.
[12]	Tatuzawa T. On Bertrand’s problem in an arithmetic pro-gression [J]. Proc Japan Acad, 1962, (38): 293-294.
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