Question 127
Let $p \ge 5$ be a positive prime number. Show that there exists an integer $t \in \{1, 2, ..., p\}$ such that the equation
$$
x^2 = y^{\frac{p-1}{2}} + t
$$
has no integer solutions.
$$
x^2 = y^{\frac{p-1}{2}} + t
$$
has no integer solutions.