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Define AAA as follows: A=10⋯0⏟n zeroes1,A=1\underbrace{0\cdots 0}_{n \text{ zeroes}}1,A=1n zeroes0⋯01, where nnn is a positive integer. Does there exist another number BBB similarly formed that is a multiple of AAA: B=10⋯0⏟m zeroes1B=1\underbrace{0\cdots 0}_{m \text{ zeroes}}1B=1m zeroes0⋯01 such that B>A?B>A?B>A?
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