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Two nonnegative integers \(a\) and \(b\) are friends if the decimal expression of \(a+b\) is formed only by 0's and I's. Suppose that \(A\) and \(B\) are two infinite sets of nonnegative integers such that \(B\) is the set of all numbers which are friends of all the elements of \(A, A\) is the set of all numbers which are friends of all the elements of \(B\). Show that one of the sets \(A, B\) contains infinitely many pairs of numbers \(x, y\) with \(x-y=1\).
in Mathematics by Platinum (138,598 points) | 25 views

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asked Jun 14, 2021 in Mathematics by Maths Genie Bronze Status (5,782 points) | 103 views

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