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UKMT Junior Mathematical Olympiad, 2023

Algebra Difficulty 1.0 Junior Prove it United Kingdom

The eleven-digit number ' $A123456789B$ ' is divisible by exactly eight of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9. Find the values of $A$ and $B$ , explaining why they must have these values.

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