no it is olympiad mathematics by m.k.singal,y?

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)

the question is rite and if i replace p(n) by 1 according to first rule of PMI then the answer is comingg to be 1 which is an integer

1/7 + 1/5+ 2/3 - 1/105=105/105=1

I f apply the formula of density=mass/volume then it shud be 54.95/7.42 which comes out to be 7.4043127cc and that doesnt  match with the answer.

Secondly,the question is to be given of atomic wt.

but the answer given to this question is 1.23 x 10/\-23 cc