hello everybody i have a question for everyone that i need help on.
the question:
show that if P is an odd prime and A is a positive integer not divisible by P (so P does not divide A), then the congruence X^2 = A (mod P) has either no solution or exactly two incongruent solutions.
ok here is what i know so far:
1.) there are exactly two incongruent solutions so the option of no solution does not exist.
2.) i know the answer should be somthing like X = +/- A (mod P) just by looking at the problem and thinking about it in my mind.
the problem:
1.) how to start the prove.
can someone please help me with this one. any hits will help.
the question:
show that if P is an odd prime and A is a positive integer not divisible by P (so P does not divide A), then the congruence X^2 = A (mod P) has either no solution or exactly two incongruent solutions.
ok here is what i know so far:
1.) there are exactly two incongruent solutions so the option of no solution does not exist.
2.) i know the answer should be somthing like X = +/- A (mod P) just by looking at the problem and thinking about it in my mind.
the problem:
1.) how to start the prove.
can someone please help me with this one. any hits will help.