Many solutions to the S-unit equation a+1=c
We show that there are arbitrarily large sets S of s primes for which the number of solutions to a + 1 = c where all prime factors of ac lie in S has ≫ exp ( s 1 / 4 / log s ) solutions.
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| Veröffentlicht in: | Acta mathematica Hungarica 2020-02, Vol.160 (1), p.153-160 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We show that there are arbitrarily large sets
S
of
s
primes for which the number of solutions to
a
+
1
=
c
where all prime factors of
ac
lie in
S
has
≫
exp
(
s
1
/
4
/
log
s
)
solutions. |
|---|---|
| ISSN: | 0236-5294 1588-2632 |
| DOI: | 10.1007/s10474-019-00948-z |