MathDB

Suppose there are

160

pigeons and

n

holes. The

1

st pigeon flies to the

1

st hole, the

2

nd pigeon flies to the

4

th hole, and so on, such that the

i

th pigeon flies to the

(i^2\text{ mod }n)

th hole, where

k\text{ mod }n

is the remainder when

k

is divided by

n

. What is minimum

n

such that there is at most one pigeon per hole?
Proposed by Christina Yao

Problem Statement