# An interesting equation in natural numbers

Let $n$ be a fixed natural number. How to solve the following equation in natural numbers: $$\frac{1}{x_1} + \frac{2}{x_2} + \cdots + \frac{n}{x_n} = 1$$ (I can find many soltions but I am looking for all solutions)

• What are $x_1...$ integers or natural numbers – Archis Welankar Jan 5 '16 at 5:21
• @ArchisWelankar natural numbers – alex alexeq Jan 5 '16 at 5:21
• It is sufficient to solve the equation. $$\frac{1}{x_1}+\frac{2}{x_2}+\frac{3}{x_3}=\frac{a}{b}$$ Number $a,b -$ will be set. Which are obtained if we ask the other numbers at their discretion. – individ Jan 5 '16 at 5:32
• You can use this formula. math.stackexchange.com/questions/450280/… – individ Jan 5 '16 at 5:44
• I see what you mean that it's trivial to write down some solutions e.g. $x_i=in$. But do you have a good reason to believe it's easy to characterize all solutions? That seems like it may be intractable. – Gregory Grant Jan 5 '16 at 6:06