Geodesic
Small Solutions of φ 1 x 1 2 + . . . + φ n xn 2 = 0
Canadian journal of mathematics, Tome 52 (2000) no. 3, pp. 613-632

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Let ${{\phi }_{1}},...,{{\phi }_{n}}\,(n\,\ge \,2)$ be nonzero integers such that the equation $$\sum\limits_{i=1}^{n}{{{\phi }_{i}}x_{i}^{2}\,=\,0}$$ is solvable in integers ${{x}_{1}},...,{{x}_{n}}$ not all zero. It is shown that there exists a solution satisfying $$0\,<\,\sum\limits_{i}^{n}{\left| {{\phi }_{i}}\left| x_{i}^{2}\,\le \,2 \right|{{\phi }_{1}}...{{\phi }_{n}}\, \right|}$$ ,and that the constant 2 is best possible.
DOI : 10.4153/CJM-2000-027-1
Mots-clés : 11E25, small solutions, diagonal quadratic forms 
Ou, Zhiming M.; Williams, Kenneth S. Small Solutions of φ 1 x 1 2 + . . . + φ n xn 2 = 0. Canadian journal of mathematics, Tome 52 (2000) no. 3, pp. 613-632. doi: 10.4153/CJM-2000-027-1
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