Let p be a prime with p \equiv 1 \pmod{4}. Determine whether there always exists a positive integer a and a divisor d \mid a^2 such that
pd \equiv -a \pmod{4a - 1}.
Let p be a prime with p \equiv 1 \pmod{4}. Determine whether there always exists a positive integer a and a divisor d \mid a^2 such that
pd \equiv -a \pmod{4a - 1}.