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On the magnitude of the integer solutions of the equationax2+by2+cz2= 0

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
1
Issue
1
Identifiers
DOI: 10.1016/0022-314x(69)90019-5
Disciplines
  • Mathematics

Abstract

Abstract A simple elementary proof is given of Holzer's theorem, namely, that if the equation ax 2 + by 2 + cz 2 = 0, taken in the normal form is solvable in integers, then a solution exists with |x| ≤ (|bc|) 1 2 , |y| ≤ (|ca|) 1 2 , |z| ≤ (|ab|) 1 2 .

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