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Nested radical redux (Posted on 2022-06-04) Difficulty: 3 of 5
Find all positive integers (x,y) that satisfy y=√(x+x√x)

Find all positive integers (x,y) that satisfy y=√(x+x√(x+x√x))

No Solution Yet Submitted by Jer    
Rating: 5.0000 (2 votes)

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re: Puzzle Solution: Part B | Comment 4 of 9 |
(In reply to Puzzle Solution: Part B by K Sengupta)

Not so fast, KS!


I'm not sure my second version is correct, either! It works for 0-3, but x=4 gives a non-integer solution. 

I was copying from rough notes, so it is possible there's a slip in the formula.

Note: It seems there was:

y=√((2x-1)^2-1)^2+(2x-1)^2-1)^2√((2x-1)^2-1)^2+(2x-1)^2-1)^2√(2x-1)^2-1)^2)) works fine.

Edited on June 4, 2022, 9:04 am
  Posted by broll on 2022-06-04 09:01:25

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