In this paper, we consider a conjecture of Erd\H{o}s and Rosenfeld when the number is a perfect square. In particular, we show that every perfect square $n$ can have at most five divisors between $\sqrt{n} - c \sqrt[4]{n}$ and $\sqrt{n} + c \sqrt[4]{n}$.
On a sufficient condition that the square root of s is simply normal to base 2, for s not a perfect square
On the simple normality to base 2 of the square root of s, for s not a perfect square
Difference of powers of consecutive primes which are perfect squares
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