Prove or disprove (I think it's true, but I don't have pencil nor paper so I can't work on this at the moment) that if

\(\dfrac{a_c}{b_c}=x_c\)

Where a,b,c,x are integers and c does not divide x without remainder; then

\(\dfrac{a_{10}}{b_{10}}=x_{10}\)

Assume:

\(a_c\) means a in base c.

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