How Does Modular Arithmetic Relate to Odd Prime Numbers?

[Daveyboy]

b>1, p an odd prime

b² = -1 mod p

if p|b² + 1
show p = 1 mod 4

I know that the order of b is 4 (mod p)

 

[Fightfish]

That's a strange approach to use...
I would do it this way: Since p is odd, and p|a^2 + 1, a must be an even number. a^2 thus = 0 (mod 4), and consequently a^2 + 1, and p are both congruent to 1 (mod 4)

 

[Daveyboy]

haha, oh man it's so obvious, I can't believe I missed it.