perplexus.info :: Just Math : A radical problem

A radical problem (Posted on 2016-11-15)

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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

analytical solution

| Comment 1 of 2

This can be rewritten as

Y = sqrt(n + Y)

Y^2 = n + Y

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

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (18)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info