MathDB

Can you pair the divisors of n such that all quotients are close to p?

Source: Francophone 2024, Senior P4

April 4, 2024

number theorynumber theory proposedprime numbersDivisors

Problem Statement

Let

p

be a fixed prime number. Find all integers

n \ge 1

with the following property: One can partition the positive divisors of

n

in pairs

(d,d')

satisfying

d<d'

and

p \mid \left\lfloor \frac{d'}{d}\right\rfloor