For n  =  1, the next integer greater than (  +  ) is 5, which is not divisible 2²  =  4.

Some mistake in the question???

for n=1

it is 4

ques is absol  ,.correct

In this question there is one hint given and that is:

first prove that (sqrt7+sqrt3)^n + (sqrt7-sqrt3)^n is an integer

then prove that he above integer is divisible by 2^2n

as,0<sqrt7-sqrt3<1

but i'm not able to understand that y sqrt7-sqrt3 since that is not the integer next greater than p(n)