Suppose \(\sqrt[2016]{\sqrt[2015]{\sqrt[...]{\sqrt[3]{\sqrt{x}}}}}=x^2-y\),

for \(x,y\in \mathbb{Z},\)

for \(x \ge 0\)

Find the number of possible values for x+y.

Guest Dec 16, 2015

edited by
Guest
Dec 16, 2015

#2**+10 **

Theoretically, it could be any positive number as X and Y are undefined and no negative can be under a square root.

BOOOOOOOOOOOM!!!!!

SpawnofAngel
Dec 16, 2015

#4**+5 **

Another way to write this is

\(x=(x^2-y)^{2016!} \)

x and y must both be integers

If x=0 and y=0 then 0=0 that works

If \(x=1\;\;and\;\;x^2-y=\pm1\)

that would work to if they are both integers that is

1-y=1

y=0

so

if x=1 and y=0 that works too

1-y=-1

2=y

so

if x=1 and y=2 that will work

and that is it

so the 3 answers are (0,0) (1,0) and (1,2)

So x+y = 0 or 1 or 3

Maybe another mathematician can do it a different / better way ??

Melody
Dec 16, 2015