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The Quarterly Journal of Mathematics 2001 52(1):107-126; doi:10.1093/qjmath/52.1.107
© 2001 by Oxford University Press
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The exceptional set in Roth's theorem concerning a cube and three cubes of primes

Xiumin Ren1

1 School of Economics, Shandong University, Jinan, Shandong 250100, P. R. China, e-mail: jyliu{at}sdu.edu.cn

It is proved that, with at most O (N 169/170) exceptions, all positive integers up to N are the sum of a cube and three cubes of primes. This improves a classical result of Roth.

Received 11 January 2000.


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