Problem 1 is fairly easy. Suppose there in a non-integral rational solution

X=a/b where b!=1, and a and b coprime.

Then multiply the equation through by b^(n-1). The first term is then not

an integer, and all the other terms are integers, and the sum is zeros, which

is impossible as the sum cannot be an integer.

Therefore if there is a rational solution it is integral.

RonL