MathDB

In many computer languages, the division operation ignores remainders. Let’s denote this operation by

//

, so for instance

13//3 = 4

. If, for some

b

a//b = c

, then we say that

c

is a near factor of

a

. Thus, the near factors of

13

are

1

2

3

4

, and

6

. Let

a

be a positive integer. Prove that every positive integer less than or equal to

\sqrt{a}

is a near factor of

a

Problem Statement