Let n N which one of the following is true?

Step-by-step solution

(a) 47^n+16 n-1 array r (48-1)^n+4(4 n)-1 48 k+(-1)^n+4 m-1 4(12 k+m)+(-1)^n-1 array 47^n+16 n-1 is divisible by 4 if n is odd. It is false for all values of n (b) 2 (4^ 2 n+1 )-3^ 3 n+1 8 4^ 2 n -3 3¹⁴ Put n=1, 8 4^2-3 3^1=8 16-9=119 119 is not divisible by 9 . (c) 4^ n+ -3 n-1 Put n=2, 4^2-3(2)-1=16-7=9 which is not divisible by 11 . (d) 3 5^ 2 n+1 +2^ 3 n+1 gathered 15 5^ 2 n +2 2^ 3 n 15 (25^n+2 (8)^n . 15 (17+8)^n+2 8^n 15 (17 k+8^n )+2 8^n 15 (17 k+8^n )+8^n(15+2) gathered =17 (15 k+8^n ) 3 5^ 3 n+1 +2^ 3 n+1