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Elliptic curves and rational distance sets
Author:
W. D. Peeples
Journal:
Proc. Amer. Math. Soc. 5 (1954), 29-33
MSC:
Primary 14.0X
MathSciNet review:
0060262
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References |
Similar Articles |
Additional Information
- [1]
Gerald
B. Huff, Diophantine problems in geometry and elliptic ternary
forms, Duke Math. J. 15 (1948), 443–453. MR 0025489
(10,14c)
- [2]
K. Mahler, Über die rationalen Punkte auf Kurven vom Geschlecht Eins, J. Reine Angew. Math. vol. 170 (1934) p. 168.
- [3]
L. J. Mordell, On the rational solutions of indeterminate equations of the third and fourth degree, Proc. Cambridge Philos. Soc. vol. 21 (1922) pp. 179-192.
- [4]
L.
J. Mordell, Rational points on cubic curves and surfaces,
Amer. Math. Monthly 51 (1944), 332–339. MR 0010155
(5,254g)
- [5]
L.
J. Mordell, On cubic equations
𝑧²=𝑓(𝑥,𝑦) with an infinity of integer
solutions, Proc. Amer. Math. Soc. 3 (1952), 210–217. MR 0047067
(13,822g), http://dx.doi.org/10.1090/S0002-9939-1952-0047067-0
- [6]
Trygve
Nagell, Sur les propriétés arithmétiques des
cubiques planes du premier genre, Acta Math. 52
(1929), no. 1, 93–126 (French). MR
1555271, http://dx.doi.org/10.1007/BF02547402
- [7]
H. Poincaré, Sur les propriétés arithmétiques des courbes algébriques, J. Math. Pures Appl. (5) vol. 7 (1901) pp. 161-233.
- [8]
G.
Sansone, Su un problema di analisi indeterminata e sui punti
razionali di una famiglia di curve ellitiche, Ann. Mat. Pura Appl. (4)
20 (1941), 105–135 (Italian). MR 0016926
(8,88c)
- [9]
André
Weil, L’arithmétique sur les courbes
algébriques, Acta Math. 52 (1929), no. 1,
281–315 (French). MR
1555278, http://dx.doi.org/10.1007/BF02547409
- [1]
- Gerald B. Huff, Diophantine problems in geometry and elliptic ternary forms, Duke Math. J. vol. 15 (1948) pp. 443-453. MR 0025489 (10:14c)
- [2]
- K. Mahler, Über die rationalen Punkte auf Kurven vom Geschlecht Eins, J. Reine Angew. Math. vol. 170 (1934) p. 168.
- [3]
- L. J. Mordell, On the rational solutions of indeterminate equations of the third and fourth degree, Proc. Cambridge Philos. Soc. vol. 21 (1922) pp. 179-192.
- [4]
- -, Rational points on cubic curves and surfaces, Amer. Math. Monthly vol. 51 (1944) pp. 332-339. MR 0010155 (5:254g)
- [5]
- -, On cubic equations
with an infinity of integer solutions, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 210-217. MR 0047067 (13:822g)
- [6]
- Trygve Nagell, Sur les propriétés arithmétiques des cubiques planes du premier genre, Acta Math. vol. 52 (1929) pp. 93-126. MR 1555271
- [7]
- H. Poincaré, Sur les propriétés arithmétiques des courbes algébriques, J. Math. Pures Appl. (5) vol. 7 (1901) pp. 161-233.
- [8]
- G. Sansone, Su un prolema di analise indeterminate e sui (punti) razionali di una formiglia di curve ellitische dipendenti da un parametra, Annali di Mathematica Pura ed Applicata vol. 4 (1941) pp. 105-135. MR 0016926 (8:88c)
- [9]
- Andre Weil, L'arithmétique sur les courbes algébriques, Acta Math. vol. 52 (1929) pp. 281-315. MR 1555278
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1954-0060262-1
PII:
S 0002-9939(1954)0060262-1
Article copyright:
© Copyright 1954 American Mathematical Society
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