1 results
Small Solutions of ϕ1x12 + . . . + ϕnxn2 = 0
-
- Journal:
- Canadian Journal of Mathematics / Volume 52 / Issue 3 / 01 June 2000
- Published online by Cambridge University Press:
- 20 November 2018, pp. 613-632
- Print publication:
- 01 June 2000
-
- Article
-
- You have access
- Export citation
-
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.
