Modular arith, number theory problem

[imranq]

Homework Statement

Find the number of roots for the equation $$x^2+1=0 \mod n \: for \: n = 8,9,10,45$$

Homework Equations

The Attempt at a Solution

I have no idea where to start. Could someone help me understand?

 

[tara123]

Do you understand what mod refers to?

 

[imranq]

yea, mod is used to represent items in terms of base n. But I don't understand how that is going to change the number of roots in the problem

 

[lanedance]

not sure but is this like modular arithmetic below?

so for the case n = 2,
try x = 0, 0²+1= 1mod2 = 1 - FALSE
try x = 1, 1²+1= 2mod2 = 0 - TRUE
x = 1 is the only for the n = 2 case

so for the case n = 3,
try x = 0, 0²+1= 1mod2 = 1 - FALSE
try x = 1, 1²+1= 2mod3 = 2 - FALSE
try x = 2, 3²+1= 2mod3 = 0 - TRUE
x = 1 is the only solution for the n = 3 case

will start getting more interesting as the square get bigger and do more "loops" in the modular arithmetic...