Question 84
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
$$
3^{k}-1=x^{n}.
$$