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‘Important’ applications of p-adic numbers outside of algebra (and number theory).
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Produce an irreducible polynomial that can’t be proved irreducible by using Eisenstein
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Bijective function on a dense set
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P-adic Arithmetic Software
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p-subgroups of automorphisms of $p$ groups
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Generalizing a problem to make it easier
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Jokes in the sense of Littlewood: examples?