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' $ DynaLite Graduate Student Seminar p-adic Numbers Carl Olimb Department of Mathematical Sciences Montana State University Monday, March 27, 4:10 – 5:00 pm 2–244 Hurst Conference Room ABSTRACT Over the last century, p-adic numbers have come to play a central role in modern number theory. The analogy between the fields Qp and R is easily understood and provides helpful information when dealing with a variety of problems. In this talk I will investigate the construction of Qp by completing Q for all of its nontrivial absolute values. Also, the similarities between the two fields Qp and R will be discussed. In particular, work will be done with Hensel’s lemma and the local/global properties of Hasse-Minkowski Theorem for three indeterminates. & %