MathDB

4

Part of 2011 Nordic

Problems(1)

Harmonic sums of relatively prime integers

Source: Nordic MO 2011 Q4

4/21/2013
Show that for any integer n≥2n \ge 2 the sum of the fractions 1ab\frac{1}{ab}, where aa and bb are relatively prime positive integers such that a<b≤na < b \le n and a+b>na+b > n, equals 12\frac{1}{2}. (Integers aa and bb are called relatively prime if the greatest common divisor of aa and bb is 11.)
number theoryrelatively primegreatest common divisornumber theory unsolved