Are there infinitely many sets of triples $\{ x,x+1,x+2\}$ that are square free? I suppose there are a series of such questions, depending on the length of the set, staring with pairs, and the power that is supposed t...--prophetes.ai

Are there infinitely many sets of triples $\{ x,x+1,x+2\}$ that are square free? I suppose there are a series of such questions, depending on the length of the set, staring with pairs, and the power that is supposed to be missing from the divisors. Here is a problem insisting on the opposite; that the numbers should all have a certain power as divisor.

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