Define the following infinite collection of subsets of the positive integers: A1 = {x|x E Z* and 0 < x < 10}, A2 = {x]x € Z* and 10 < x < 20}, A3 = {x\x € Z* and 20 < x < 30}, .. Let R be the “in the same subset" relation. a R b if and only if 3k such that a E Ar and b E Ar.

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Q: Prove that there are integers x and y such that 10x-13y=1

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