Abstract
Essentially sharp bounds for small prime solutionsp j ,q i of the following two different types of equations are obtained.
where the two sets of integers,a 1,...,a 5,b andc 1,c 2,c 3,d satisfy the congruent solubility condition andk≥1 is an integer. These results are comparable with the well-known Meyer theorem on indefinite integral quadratic form and the celebrated Vinogradov three primes theorem.
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References
Davenport, H.: Multiplicative Number Theory (2nd ed.). Berlin-Heidelberg-New York: Springer. 1980.
Ghosh, A.: The distribution of αp 2 modulo 1. Proc. London Math. Soc. (3),42, 252–269 (1981).
Hua, L. K.: Additive Theory of Prime Numbers. Providence, R. I.: Amer. Math. Soc. 1965.
Hua, L. K.: Some results in the additive prime-number theory. Quart. J. Math. Oxford Ser.9, 68–80 (1938).
Mordell, L. J.: Diophantine Equations. London-New York: Academic Press. 1969.
Liu, M. C., Tsang, K. M.: Small prime solutions of linear equations. In: Number Theory (Eds.J.-M. de Koninck, C. Levesque), pp. 595–624. Berlin: W. de Gruyter. 1989.
Liu, M. C., Tsang K. M.: On pairs of linear equations in three prime variables and an application to Goldbach's problem. J. reine angew. Math.399, 109–136 (1989).
Vinogradov, I. M.: Elements of Number Theory. New York: Dover Publ. 1954.
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Liu, MC., Tsang, KM. Small prime solutions of some additive equations. Monatshefte für Mathematik 111, 147–169 (1991). https://doi.org/10.1007/BF01332353
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DOI: https://doi.org/10.1007/BF01332353