## anonymous 3 years ago How many natural numbers $$n$$ are there such that$\sqrt{n+\sqrt{n+\sqrt{n+\sqrt{n+...}}}}$is natuaral too.

1. hartnn

p^2 - p - n =0

2. anonymous

n=2,6 gives 2 and 3 ,... ??? are there more numbers?

3. anonymous

|dw:1347788157019:dw| then, a^2=n+a

4. anonymous

Now, a and n has to be natural too

5. jiteshmeghwal9

but that's the value of the total equation @sauravshakya :(

6. anonymous

n is natuaral... a has to be natural :)

7. anonymous

Ya.......... thinking on it...... I think it will lead to solution

8. anonymous

n=a^2-a

9. jiteshmeghwal9

that's it because if we right the equation as$\sqrt{n+\sqrt{n+\sqrt{n.....}}}=x$then we find the value of 'x' to get the answer & u did the same.

10. anonymous

If a=2 then n=2, If a=3 then n=6...

11. anonymous

infinite solutions

12. anonymous

If a=4 then n=12, If a=5 then n=20 ...

13. anonymous

right? @mukushla

14. anonymous

right :)