MathDB
1/x_1 + 1/x_2 +... + 1/x_n = 1997/1998

Source: 1998 Swedish Mathematical Competition p5

April 2, 2021
number theory

Problem Statement

Show that for any n>5n > 5 we can find positive integers x1,x2,...,xnx_1, x_2, ... , x_n such that 1x1+1x2+...+1xn=19971998\frac{1}{x_1} + \frac{1}{x_2} +... + \frac{1}{x_n} = \frac{1997}{1998}. Show that in any such equation there must be two of the nn numbers with a common divisor (>1> 1).
Back to ProblemsView on AoPS