×

# Can we generalize it?

Solve :$$\displaystyle \frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_n}=1$$ for positive integers $$(a_1,a_2,a_3,\cdots,a_n)$$ .

There could be a remarkable proof/method.

8 months, 2 weeks ago

Sort by:

Sylvester's sequence! · 8 months ago

What about 1/(n)(n+1)? Or for generalization, Leibniz's triangle? · 7 months, 3 weeks ago

Yes I've tried that and thanks for mentioning too , but I think those are not only solutions. Indeed suppose we are to generalize it for 5 variables & Leibniz's triangle gives us 5 different values only. But there exists many more pairs than that · 7 months, 3 weeks ago