Abstract
The main result is thatr quadratic forms in more than 4r 2+4r variables possess a common nontrivialp-adic zero.
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Schmidt, W.M. Simultaneousp-adic zeros of quadratic forms. Monatshefte für Mathematik 90, 45–65 (1980). https://doi.org/10.1007/BF01641711
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DOI: https://doi.org/10.1007/BF01641711