Question 78
Consider the equation
$$
x^{2001} = y^{x}.
$$
a. Determine all $(x, y)$ pairs of solutions in which $x$ is a prime number and $y$ is a positive integer.
b. Determine all pairs $(x, y)$ of solutions in which $x$ and $y$ are positive integers.
(Remember that $2001 = 3 \cdot 23 \cdot 29$)
$$
x^{2001} = y^{x}.
$$
a. Determine all $(x, y)$ pairs of solutions in which $x$ is a prime number and $y$ is a positive integer.
b. Determine all pairs $(x, y)$ of solutions in which $x$ and $y$ are positive integers.
(Remember that $2001 = 3 \cdot 23 \cdot 29$)