Abstract: We introduce the notion of p-adic absolute value on the rationals. We prove that, up to equivalence, these and the usual Euclidean absolute value are the only non-trivial absolute values on the rationals. Then we discuss the completion of the rationals under the p-adic absolute value to obtain p-adic numbers. Finally we discuss applications of p-adic numbers to problems in number theory, in particular, we explore the local to global principle.
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