Abstract
We prove that any positive rational number is the sum of distinct unit fractions with denominators in {p−1:p prime}. The same conclusion holds for the set {p−h:p prime} for any h∈Z∖{0}, provided a necessary congruence condition is satisfied. We also prove that this is true for any subset of the primes of relative positive density, provided a necessary congruence condition is satisfied.
| Original language | English |
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| Pages (from-to) | 1-11 |
| Number of pages | 11 |
| Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
| DOIs | |
| Publication status | Published - 2 Apr 2024 |
Keywords
- number theory
- prime numbers
- unit fractions