2^n = n^2

[abehrman]

for how many integers is 2^n = n^2?

I can only find one, but the answer is 2.

[oana_mitrache]

the answers are:2 and 4

[zchampz]

Yep.
n=2 => 2^2 = 2^2 = 4
n=4> 2^4 = 4^2 = 16

I am wondering is there any better approach/trick to solve these kind of problems or just we have to plug-in numbers and verify?

[agha79]

I lined up integers 1, 2, 3, 4, 5, 6, 7, and start plugging in. After 4 it was quite clear nothing else would work. I think it took me less than 60 secs to come to the answer. Not sure if there is another approach but brute force here is not that time consuming.

[RonPurewal]

I lined up integers 1, 2, 3, 4, 5, 6, 7, and start plugging in. After 4 it was quite clear nothing else would work. I think it took me less than 60 secs to come to the answer. Not sure if there is another approach but brute force here is not that time consuming.

good for you.

the test will do this on occasion: include problems that effectively CANNOT be solved by algebra, but whose solutions may be deduced very quickly by simple enumeration (listing of possibilities).

if an algebraic solution is ever not forthcoming, don't try to force one; it may not exist!