Bounds for the least solutions of homogeneous quadratic equations
Bounds for the least solutions of homogeneous quadratic equations
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齐次二次方程最小解的界
DOI：
10.1017/s0305004100030188
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发表时间：
1955
影响因子：
0.8
通讯作者：
J. Cassels
中科院分区：
文献类型：
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作者：
J. Cassels
对于三元对角形式，这样的边界已经由Axel Thue(4)给出，最近由Holzer (1), Mordell(2)和Skolem(3)给出，但这些只导致一般三元形式的坏估计。据我所知，目前还没有给出评估。在这里我推广了Thue的证明方法：定理。假设n≥2，f(i) = 0。那么就有f(a) = 0的积分解
In this note I obtain bounds for the least integral solutions of the equation in terms of For ternary diagonal forms, such bounds have been given by Axel Thue (4) and, more recently, by Holzer (1), Mordell (2) and Skolem (3), but these lead only to bad estimates for general ternaries. So far as I know there have not been given estimates for n≽4. Here I generalize Thue's method to prove: Theorem. Suppose that n ≥ 2 and that f(ɛ) represents zero. Then there is an integral solution of f(a) = 0 with