Solutions to Diophantine Equation x (x + 1) = y (y + 5) (y + 10) (y + 15)/Historical Note

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Historical Note on Solutions to Diophantine Equation $x \left({x + 1}\right) = y \left({y + 5}\right) \left({y + 10}\right) \left({y + 15}\right)$

According to David Wells in his Curious and Interesting Numbers, 2nd ed. of $1997$, this result appeared in Acta Arithmetica on page $194$ of volume $7$.

However, this contributor has tried to identify the article in question, and it appears to have nothing to do with the theorem discussed here.