MathDB

Harmonic sums of relatively prime integers

Source: Nordic MO 2011 Q4

April 21, 2013

number theoryrelatively primegreatest common divisornumber theory unsolved

Problem Statement

Show that for any integer

n \ge 2

the sum of the fractions

\frac{1}{ab}

, where

a

and

b

are relatively prime positive integers such that

a < b \le n

and

a+b > n

, equals

\frac{1}{2}

. (Integers

a

and

b

are called relatively prime if the greatest common divisor of

a

and

b

1