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AKG

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[tex]x = 1 + a_1p^1 + \dots + a_{m-1}p^{m-1}[/tex]

for [itex](a_1,\, a_2,\, \dots ,\, a_{m-1}) \in (\mathbb{Z}_p)^{m-1}[/itex]. I haven't been able to get anywhere this problem. I've tried to see if [itex]1 + p + p^2 + /dots + p^{m-1}[/itex] generates the group, but haven't had any success in doing so, and I'm not even sure that it does. I've also considered inductive proofs without success. Any hints?