The Unheard Islander

A puzzle by Edward J. Barbeau, from the February 2007 issue of Crux Mathematicorum:

A certain familiar island is inhabited by knights, who can only speak the truth, and knaves, who can only lie. One day a visitor meets three inhabitants, A, B, and C. The visitor asked, “How many knights are there among you three?”

A gave an answer, which the visitor didn’t hear. When the visitor asked B what A had said, B replied, “A said that there is one knight among us.” At this C said, “Don’t believe B. He is lying.”

What are B and C?

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