| Title:
|
A note on the number of $S$-Diophantine quadruples (English) |
| Author:
|
Luca, Florian |
| Author:
|
Ziegler, Volker |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
22 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
49-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(a_1,\dots , a_m)$ be an $m$-tuple of positive, pairwise distinct integers. If for all $1\leq i< j \leq m$ the prime divisors of $a_ia_j+1$ come from the same fixed set $S$, then we call the $m$-tuple $S$-Diophantine. In this note we estimate the number of $S$-Diophantine quadruples in terms of $|S|=r$. (English) |
| Keyword:
|
Diophantine equations |
| Keyword:
|
$S$-unit equations |
| Keyword:
|
$S$-Diophantine tuples |
| MSC:
|
11D45 |
| MSC:
|
11N32 |
| idZBL:
|
Zbl 06359722 |
| idMR:
|
MR3233726 |
| . |
| Date available:
|
2014-08-27T08:58:33Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143905 |
| . |
| Reference:
|
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| Reference:
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