The number of equations c=a+b satisfying the abc-conjecture
| dc.creator | Petridi, Constantin M. | |
| dc.date | 2009-04-13 | |
| dc.date.accessioned | 2026-07-07T13:03:24Z | |
| dc.date.available | 2026-07-07T13:03:24Z | |
| dc.description | We prove that for a positive integer $c$ and any given $\varepsilon$, $0<\varepsilon<1$, the number $N(c)$ of equations $c=a+b$, $a<b$, with positive coprime integers $a$ and $b$, which satisfy the inequality $$c < R(c)^{\frac{\varepsilon}{1+\varepsilon}}R(a)^{\frac{1}{1+\varepsilon}}R(b)^{\frac{1}{1+\varepsilon}},$$ where R(n) is the radical of $n$, is for $c\to\infty$ $$N(c)=(1-\varepsilon)\frac{ϕ(c)}{2}+O\Bigl(\frac{ϕ(c)}{2}\Bigr).$$ An analogue for the abc-conjecture inequality $c<R(abc)^{1+\varepsilon}$ (without a constant factor) will also be proved. | |
| dc.identifier | https://arxiv.org/abs/0904.1935 | |
| dc.identifier | http://arxiv.org/abs/0904.1935 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226789 | |
| dc.subject | Number Theory | |
| dc.title | The number of equations c=a+b satisfying the abc-conjecture | |
| dc.type | text |