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A radical problem (Posted on 2016-11-15) Difficulty: 2 of 5
Let n be a 5-digit positive integer.
Given the infinitely nested radical expression below:

Y = sqrt(n+ sqrt(n+ sqrt(n+… sqrt(n+… ,-

What is the maximal value of n, such that Y is a positive integer?

No Solution Yet Submitted by Ady TZIDON    
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Solution analytical solution | Comment 1 of 2
This can be rewritten as 
Y = sqrt(n + Y)
or
Y^2 = n + Y
or
n = Y(Y-1)

sqrt (99999) = 316.3

317*316 is over 100000,

so n = 316*315 = 99,540 and Y = 316

Edited on November 16, 2016, 7:36 am
  Posted by Steve Herman on 2016-11-15 08:22:13

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