Can there exist two distinct integers $x$ and $y$ such that $x,y$ have the same prime factors, $x+1,y+1$ have the same prime factors, and $x+2,y+2$ also have the same prime factors?

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1True ↔2  ∃ x y,3    x ≠ y ∧4      x.primeFactors = y.primeFactors ∧5        (x + 1).primeFactors = (y + 1).primeFactors ∧ (x + 2).primeFactors = (y + 2).primeFactors

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