Romania 2013 p4 grade 12

Given n\ge 2 a natural number, (K,+,\cdot ) a body with commutative property that \underbrace{1+...+}_{m}1\ne 0,m=2,...,n,f\in K[X] a polynomial of degree n and G a subgroup of the additive group (K,+,\cdot ), G\ne K.Show that there is a\in K so f(a)\notin G.

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