mukushla
How many natural numbers \(n\) are there such that\[\sqrt{n+\sqrt{n+\sqrt{n+\sqrt{n+...}}}}\]is natuaral too.



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hartnn
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p^2  p  n =0

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

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

sauravshakya
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Now, a and n has to be natural too

jiteshmeghwal9
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but that's the value of the total equation @sauravshakya :(

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

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

sauravshakya
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n=a^2a

jiteshmeghwal9
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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.

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

sauravshakya
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infinite solutions

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

sauravshakya
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right? @mukushla

mukushla
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right :)