Share
Explore BrainMass

Number Theroy

Is there a perfect square n^2 such that

n^2 = -1 (mod p) for

p=3
p=5
p=7
p=11
p=13
p=17
p=19?

Can you characterize the primes for which n^2 = -1 (mod p) has a solution?

Solution Preview

Sol: If a = b (mod k), then b = a + mk, where m is an integer.
Here, n^2 = -1 (mod p) implies that -1 = n^2 + mp, where m is an ...

$2.19