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

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hartnn Group TitleBest ResponseYou've already chosen the best response.0
p^2  p  n =0
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
n=2,6 gives 2 and 3 ,... ??? are there more numbers?
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
dw:1347788157019:dw then, a^2=n+a
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Now, a and n has to be natural too
 2 years ago

jiteshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
but that's the value of the total equation @sauravshakya :(
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
n is natuaral... a has to be natural :)
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Ya.......... thinking on it...... I think it will lead to solution
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
n=a^2a
 2 years ago

jiteshmeghwal9 Group TitleBest ResponseYou've already chosen the best response.0
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.
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
If a=2 then n=2, If a=3 then n=6...
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
infinite solutions
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
If a=4 then n=12, If a=5 then n=20 ...
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
right? @mukushla
 2 years ago
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