Consider the mapping ϕ : Z [ x ] → Z k [ x ] defined by ϕ ( a 0 + a 1 x + ⋅ ⋅ ⋅ + a n x n ) = [ a 0 ] + [ a 1 ] x + ⋅ ⋅ ⋅ + [ a n ] x n , where [ a i ] denotes the congruence class of Z k that contains a i . Prove that φ is an epimorphism from Z [ x ] to Z k [ x ] .
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