Small prime solutions of quadratic equations II

Authors:
Kwok-Kwong Stephen Choi and Jianya Liu

Journal:
Proc. Amer. Math. Soc. **133** (2005), 945-951

MSC (2000):
Primary 11P32, 11P05, 11P55

Published electronically:
November 19, 2004

MathSciNet review:
2117193

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be non-zero integers and any integer. Suppose that and for . In this paper we prove that (i) if the are not all of the same sign, then the above quadratic equation has prime solutions satisfying and (ii) if all the are positive and , then the quadratic equation is soluble in primes Our previous results are and in place of and above, respectively.

**1.**Kwok-Kwong Stephen Choi and Jianya Liu,*Small prime solutions of quadratic equations*, Canad. J. Math.**54**(2002), no. 1, 71–91. MR**1880960**, 10.4153/CJM-2002-004-4**2.**Harold Davenport,*Multiplicative number theory*, 2nd ed., Graduate Texts in Mathematics, vol. 74, Springer-Verlag, New York-Berlin, 1980. Revised by Hugh L. Montgomery. MR**606931****3.**L. K. Hua, Some results in the additive prime number theory, Quart. J. Math. (Oxford) 9(1938), 68-80.**4.**Jianya Liu,*On Lagrange’s theorem with prime variables*, Q. J. Math.**54**(2003), no. 4, 453–462. MR**2031178**, 10.1093/qjmath/54.4.453**5.**J. Y. Liu and T. Zhan, An iterative method in the Waring-Goldbach problem, to appear.

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Additional Information

**Kwok-Kwong Stephen Choi**

Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Email:
kkchoi@cecm.sfu.ca

**Jianya Liu**

Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China

Email:
jyliu@sdu.edu.cn

DOI:
http://dx.doi.org/10.1090/S0002-9939-04-07784-6

Received by editor(s):
February 3, 2003

Published electronically:
November 19, 2004

Additional Notes:
The first and second authors were supported by the NSERC and the NSF of China (Grant #10125101), respectively

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.