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==Statement of the theorem==
Let '''x''' = ''x''<sub>1</sub>, …, ''x''<sub>''n''</sub> denote a collection of ''n'' [[indeterminate (variable)|indeterminant]]s, ''k''['''x'''] the [[ring (mathematics)|ring]] of formal power series with indeterminants '''x''' over a field ''k'', '''y''' = ''y''<sub>1</sub>, …, ''y''<sub>''m''</sub> a different set of indeterminants, ''f''('''x''', '''y''') = 0 a system of polynomial equations over ''k''['''x''', '''y'''], and ''c'' a positive [[integer]]. Then given a formal power series solution '''ŷ'''('''x''') ∈ ''k''[['''x''']] there is an algebraic solution '''y'''('''x''') consisting of algebraic functions such that '''ŷ'''('''x''') ≡ '''y'''('''x''') mod ('''x''')<sup>''c''<sup>.
==Discussion==
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