Can you help me with this math problem :
Each of the $K$ knights from the round table needs to choose a card which is marked with a number from $1$ to $N$, $N \ge K$. The cards all have a different number.
King Arthur will cancel the conquest if the knights choose the cards in a way that the product of the number that the knight has (marked with $A$), and the number of the knight to the left of him (marked with $B$), subtracted by $1$, is divisible by $N$. Is it possible for the conquest to be cancelled?
Mathematically written, is it possible that $~~~N|A(B - 1)~~$ ?
Any help is appreciated. Thank you in advance.
What if one of the Knights draws the $N$ card?