Wuhan University Journal of Natural Sciences

, Volume 24, Issue 3, pp 229–232

# An Equivalent Form of Strong Lemoine Conjecture and Several Relevant Results

• Shaohua Zhang
Mathematics

## 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 primecounting function

O 156

## Notes

### Acknowledgements

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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