Question: Let A be the 10-adic numbers. Prove that there are two elements a, b EA of A such that a a #0 and b

Let A be the 10-adic numbers. Prove that there are two elements

Let A be the 10-adic numbers. Prove that there are two elements a, b EA of A such that a a #0 and b #0 7 ab=0 . [Notice that this means that A is not a field, because if ab=0 then 2 but 0 and b can't have multiplicative inverses: ab:

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