On cubic polynomials
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- Schmidt, W.M. Monatshefte für Mathematik (1982) 93: 329. doi:10.1007/BF01295233
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It is shown that a system ofr homogeneous cubic equations with rational coefficients has a nontrivial solution in rational integers if the number of variables is at least (10r)5. For most such systems, an asymptotic formula holds for the numberzPof solutions whose components have modulus <P.