Is calculating $a^2 \equiv p-5 \pmod{p} $ same as calculating $a^2 \equiv 5 \pmod{p} $ ?My code (using quadratic residue method) returns same answers corresponding to both the equations for any odd prime $p$.
For example :-
For $a^2 \equiv 99986 \pmod{99991} $, my $a$ comes out to be 10104.
For $a^2 \equiv 5 \pmod{99991} $, my $a$ comes out to be 10104.