The positive integral points on the elliptic curve y 2 = (x + 4)(x 2 − 4x + 5)
In this paper, we studied the elliptic curve y 2 = ( x – a )( x 2 + ax + r ), a , r ∈ Z + in the case of a = 6, r = 7 which has no relevant conclusions up to now. And we obtained the conclusion of the integer points on Elliptic y 2 = ( x – 6)( x 2 + 6 x + 7 ), elliptic curve in title has only one in...
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| Veröffentlicht in: | Journal of physics. Conference series 2019-06, Vol.1213 (4), p.42008 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we studied the elliptic curve
y
2
= (
x
–
a
)(
x
2
+
ax
+
r
),
a
,
r
∈
Z
+
in the case of
a
= 6,
r
=
7
which has no relevant conclusions up to now. And we obtained the conclusion of the integer points on Elliptic
y
2
= (
x
– 6)(
x
2
+ 6
x
+
7
), elliptic curve in title has only one integer point (
x
,
y
) = (6,0) were proved with the help of the elementary methods such as congruence and Legendre symbol. |
|---|---|
| ISSN: | 1742-6588 1742-6596 |
| DOI: | 10.1088/1742-6596/1213/4/042008 |