\[\begin{align} 1+1 \times 2 \times 3 \times 4 &= 5^2 \\ 1+2 \times 3 \times 4 \times 5 &= 11^2 \\ 1 + 3 \times 4 \times 5 \times 6 &= 19^2 \end{align}\]

Is 1 plus the product of four consecutive integers always a perfect square?

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