If 2.4^ 2 n +1 +3^ 3 n +1 is divisible by k for all n N , then k=

Step-by-step solution

Let P (x)=2.4^ 2 n +1 +3^ 3 n +1 =2^ 4 n +3 +3^ 3 n +1 aligned & P(1)=2^7+3^4=128+81=209 & P(2)=2¹¹+3^7=2048+2187=4235 aligned H.C.F. of 209 and 435 is 11 So, P (x) is divisible by 11 .