Oh my, why am I being kept in the museum for so long?

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There are two artifacts in the museum. One of the artifacts has an age of ( A B C ) k (ABC)_k , the other one has an age of ( C B A ) k (CBA)_k . If their difference in age is ( 776 ) k 2 (776)_{\frac{k}{2}} , find k k .


The answer is 16.

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