For how many integers n is 2^n = n^2 ?
Options:  A) None  B) One  C) Two  D) Three  E) More than Three
=&gt; 2^n = n^2   Taking nth root on both sides   =&gt; 2 = (n^2)^1/n   =&gt; 2 = n ^ 2/n   Lets consider positive even multiples of 2 for n (since LHS = 2)   For n = 2   =&gt; 2 = 2 ^ 2/2 - First value that satisfier   For n = 4   =&gt; 2 = 4 ^ 2/4 - Second value that satisfier   For n = 8   =&gt; 2 = 8 ^ 2/8 - Does Not satisfy   For n = 16   =&gt; 2 = 16 ^ 2/16 - Does Not satisfy   Two values. Ans = Two
<result>C</result>
For how many integers n is 2^n = n^2 ?