The impossibility of exactly simplifying the floor quotient below the square root
Let ppp be a prime number and let aaa be an integer satisfying 1<a<p1<a<p1<a<p. Consider the quotient ⌊pa⌋\left\lfloor \frac{p}{a}\right\rfloor⌊ap⌋ for a≤⌊p⌋a\leq\left\lfloor\sqrt{p}\right\rfloora≤⌊p⌋.…