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5

Part of 1998 Swedish Mathematical Competition

Problems(1)

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

Source: 1998 Swedish Mathematical Competition p5

4/2/2021
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).
number theory