Question

find \(k\) so that
\[2^k+2^{34}+2^{37}\] is a perfect square

Answer 1

i have an answer, want to know if there is another method

Answer 2

let k=34+y then, 2^(34+y) +2^34 +2^37 = 2^34 ( 2^y +9)

Answer 3

I guess that would simplify the question

Answer 4

so y= 4

Answer 5

yeah that is pretty much the same method i used,
thanks

Answer 6

thus k = 34+4=38

Answer 7

wrote \(2^{34}(1+2^3+2^n)\) and found \(n=4\)
i was wondering if there was some kind of other reasoning

Answer 8

I finally understood this. lol (after being afk).