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Line 17: :''f''('''x''', '''y''') = 0 be a system of [[polynomial equation]]s 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~~function]]s such that :'''ŷ'''('''x''') &equiv; '''y'''('''x''') mod ('''x''')<sup>''c''<sup>.

Artin approximation theorem: Difference between revisions