Analytically determine all possible integer solutions (x,y) of each of the following equations:

(A) √(x+ √(x+ √( x +......+ √(x + √x))))) = y

(B) √(x+ √(x+ √(x + √(x ......+ √(x + √(2x))))) = y, with x < 180,000

The square root symbol in the each of the above relationships is repeated 2007 times.

(In reply to a partial solution to B by Daniel)

I don't think you'll find that to be the case because:

I think you wanted Z(0) = √(2x) which leads to:
√(2x)=√(x+√(2x))
2x=x+√(2x)
x=√(2x)
x²=2x
x=2

And in fact, x=y=2 works

Posted by Joel on 2007-02-20 02:38:05