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Let A be a 10-adic number, not a zero divisor. Proof that a 10-adic number B is dividible by A if 2^q*5^p*B has ends with p+q zeroes.

My work so far:

Because A is not a zero divisor, it is not dividible by all powers of 2 nor 5, so it follows from a theorem that A = 2^q*5^p*C with C invertible and p and q natural numbers. Now I have no clue how to connect this with 0. If anybody could help me out, I would be very grateful.

Thanks in advance.

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# P-adic number problem

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