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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Science China Press

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10.1007/bf01910730

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1869-1862

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Small prime solutions to cubic equations

Authors: LiLu Zhao
Publish Date: 2016/05/10
Volume: 59, Issue: 10, Pages: 1909-1918
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Abstract

Let a 1 a 9 be nonzero integers not of the same sign and let b be an integer Suppose that a 1 a 9 are pairwise coprime and a 1 + · · · + a 9 ≡ b mod 2 We apply the padic method of Davenport to find an explicit P = Pa 1 a 9 n such that the cubic equation a 1 p 1 3 + · · · + a 9 p 9 3 = b is solvable with p j ≪ P for all 1 ≤ j ≤ 9 It is proved that one can take P = max a 1 a 9 c with c + b1/3 with c = 2 This improves upon the earlier result with c = 14 due to Liu 2013

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