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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.03218 |
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Table of Contents:
- For two relatively prime square-free positive integers $a$ and $b$, we study integers of the form $a p+b P_{2}$ and give a new lower bound for the number of such representations, where $a p$ and $b P_{2}$ are both square-free, $p$ denote a prime, and $P_{2}$ has at most two prime factors. We also consider some special cases where $p$ is small, $p$ and $P_2$ are within short intervals, $p$ and $P_2$ are within arithmetical progressions and a Goldbach-type upper bound result. Our new results generalize and improve previous results.