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The Quarterly Journal of Mathematics 2000 51(4):451-464; doi:10.1093/qjmath/51.4.451
© 2000 by Oxford University Press
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Some Sums of Two Rational Cubes

Daniel R. Coward1

1 3591 22nd Street, San Francisco, CA 94114, USA

This paper establishes the result that numbers of the shape 52p(p {equiv} 2 mod9)and 52p2(p {equiv} 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.

Received 21 June, 1994. Revised 31 May, 1999.


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