Geodesic
Small Prime Solutions of Quadratic Equations
Canadian journal of mathematics, Tome 54 (2002) no. 1, pp. 71-91

Voir la notice de l'article provenant de la source Cambridge University Press

Let ${{b}_{1}},...,{{b}_{5}}$ be non-zero integers and $n$ any integer. Suppose that ${{b}_{1}}+\cdot \cdot \cdot +{{b}_{5}}\equiv n$ (mod 24) and $\left( {{b}_{i}},{{b}_{j}} \right)=1$ for $1\le i . In this paper we prove that (i) if all ${{b}_{j}}$ are positive and $n\gg \max {{\left\{ \left| {{b}_{j}} \right| \right\}}^{41+\varepsilon }}$ , then the quadratic equation ${{b}_{1}}p_{1}^{2}+\cdot \cdot \cdot +{{b}_{5}}p_{5}^{2}=n$ is soluble in primes ${{p}_{j}}$ , and (ii) if ${{b}_{j}}$ are not all of the same sign, then the above quadratic equation has prime solutions satisfying ${{p}_{j}}\ll \sqrt{\left| n \right|}+\max {{\left\{ \left| {{b}_{j}} \right| \right\}}^{20+\varepsilon }}$ .
DOI : 10.4153/CJM-2002-004-4
Mots-clés : 11P32, 11P05, 11P55 
Choi, Kwok-Kwong Stephen; Liu, Jianya. Small Prime Solutions of Quadratic Equations. Canadian journal of mathematics, Tome 54 (2002) no. 1, pp. 71-91. doi: 10.4153/CJM-2002-004-4
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