Question 93
a. Determine all pairs $(x, k)$ of positive integers that satisfy the equation
$$
3^{k}-1=x^{3}.
$$
b. Prove that if $n$ is an integer greater than 1 and different from 3 there are no $(x, k)$ pairs of positive integers that satisfy the equation
$$
3^{k}-1=x^{n}.
$$
$$
3^{k}-1=x^{3}.
$$
b. Prove that if $n$ is an integer greater than 1 and different from 3 there are no $(x, k)$ pairs of positive integers that satisfy the equation
$$
3^{k}-1=x^{n}.
$$