Which property characterizes the ppp-adic absolute value ∣n∣p|n|_p∣n∣p for prime ppp?
∣n∣p=n|n|_p = n∣n∣p=n for all positive integers
∣pk∣p=pk|p^k|_p = p^k∣pk∣p=pk for positive kkk
∣pk∣p=p−k|p^k|_p = p^{-k}∣pk∣p=p−k — higher powers of ppp have smaller ppp-adic absolute value
∣n∣p=∣n∣|n|_p = |n|∣n∣p=∣n∣ for all integers