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.

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.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestSylvester's sequence! – Ashu Dablo · 12 months ago

Log in to reply

What about 1/(n)(n+1)? Or for generalization, Leibniz's triangle? – Sal Gard · 11 months, 3 weeks ago

Log in to reply

– Aditya Narayan Sharma · 11 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 thatLog in to reply

How should we ? It's Its ...... How ? – Sayandeep Ghosh · 1 year ago

Log in to reply