MathDB

Prove that there is a positive integer

M

for which the following statement holds: For all prime numbers

p

, there is an integer

n

for which

\sqrt{p} \le n \le M\sqrt{p}

and

p \mod n \le \frac{n}{2020}

.
Note: Here,

p \mod n

denotes the unique integer

r \in {0, 1, ..., n - 1}

for which

n|p -r

. In other words,

p \mod n

is the residue of

p

upon division by

n

Problem Statement