Some Sums of Two Rational Cubes
This paper establishes the result that numbers of the shape 52p(p ≡ 2 mod9)and 52p2(p ≡ 5 mod9), where pa prime, are expressible as the sum of two rational cubes by finding modular parametrizations of the corresponding elliptic curves, picking special complex points on the curve and manipulating the...
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| Veröffentlicht in: | Quarterly journal of mathematics 2000-12, Vol.51 (4), p.451-464 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | This paper establishes the result that numbers of the shape 52p(p ≡ 2 mod9)and 52p2(p ≡ 5 mod9), where pa prime, are expressible as the sum of two rational cubes by finding modular parametrizations of the corresponding elliptic curves, picking special complex points on the curve and manipulating them to produce rational points thereon. |
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| ISSN: | 0033-5606 1464-3847 |
| DOI: | 10.1093/qjmath/51.4.451 |