For which of the following “n” is the number 2^74 +2^2058+2^2n is a perfect square? Choose one
A) 22777 B) 2686 C) 8667 D) 2020 E) 99771
2^74 +2^2058+2^2n = K2K2   2^74 +2^2058+2^2n = (237)2+22058+(2n)2(237)2+22058+(2n)2   We try to write this expression as (a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2   Now a = 237237, 2ab = 2205822058 and b = 2n2n   Substituting the value of a in 2ab, we get b = 2020   Ans: 2020
<result>D</result>
For which of the following “n” is the number 2^74 +2^2058+2^2n is a perfect square?