For every integer n, the expression h(n) = (2+ square root of 3)^n is an integer by mathematical induction?

Answer 1

For a proof by induction, you must prove it for a base case (n=1) and then assume it for n and prove it follows for n+1.

However, I can't prove it for n=1:
(2+√3)^1 is *not* an integer.

Did you mean prove that it is *not* an integer?

Answer 2

This is not true for n = 1 or 2.
Something wrong in the question.