An Equivalent Form of Strong Lemoine Conjecture and Several Relevant Results
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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 wordsLemoine Conjecture Dusart’s inequality Rosser-Schoenfeld’s inequality Euler totient function primecounting function
CLC numberO 156
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The author is particularly indebted to the referees for their comments improving the proof of the Theorem 2. Thank LIU Shuhua for verifying that every odd n can be represented as 2x+y for 105<n<3×109, where x and y are coprime composite numbers, and for checking Strong Lemoine Conjecture on a computer to be valid for all odd n up to 109.
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