Question 20
Determine the smallest positive integer $k$ so that the equation
$$
2002x + 273y = 200201 + k
$$
have integer solutions, and for that value of $k$, find the number of solutions $(x, y)$ with $x, y$ positive integers that the equation has.
$$
2002x + 273y = 200201 + k
$$
have integer solutions, and for that value of $k$, find the number of solutions $(x, y)$ with $x, y$ positive integers that the equation has.