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武汉大学学报 英文版 | Wuhan University Journal of Natural Sciences
Wan Fang
Wuhan University
Latest Article
An Equivalent Form of Strong Lemoine Conjecture and Several Relevant Results
ZHANG Shaohua
School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408102, China
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
[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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