Let f ( x ) = 2 x n + λ , λ ∈ ℝ , n ∈ ℕ , and f ( 4 ) = 133 , f ( 5 ) = 255 . Then the sum of all the positive integer divisors of ( f ( 3 ) - f ( 2 ) ) is

Step-by-step solution

f ( x ) is given as f ( x ) = 2 x n + λ ,   λ ∈ R ,   n ∈ N ∵   f ( 4 ) = 133 ⇒ 133 = 2 × 4 n + λ                             . . . ( 1 ) ∵   f ( 5 ) = 255 ⇒ 255 = 2 × 5 n + λ                             . . . ( 2 ) Now, ( 2 ) - ( 1 ) 122 = 2 5 n - 4 n ⇒ 5 n - 4 n = 61 ∴ n = 3 &#16