Question 43
Let $\varepsilon$ be a positive real number. A positive integer will be called $\varepsilon$-squarish if it is the product of two integers $a$ and $b$ such that $1 \lt a \lt b \lt (1 + \varepsilon)a$. Prove that there are infinitely many occurrences of six consecutive $\varepsilon$-squarish integers.