Discrete Math - Modular Arithmetic

[hammonjj]

Homework Statement

For which values of n≥2 does the implication:

axb=0 ⇔ a=0 or b=0

For some Zn (n should be a subscript)

NOTE: For the a x b, the x should be the x that has a circle around it. I didn't see that symbol in the "quick symbols" :)

Homework Equations

I know that this is true when n is a prime (answer in back of book), but I don't understand why. For example, if a=5 and b = 4, then that would also be 0 for n=5, right? Do I just not understand how to do modular arithmetic?

Thanks!

 

[HallsofIvy]

What is your definition of that symbol? I would have interpreted as a "tensor product" but that doesn't really make sense here. I suspect it is a "special operation" your text is defining for this problem.

 

[tiny-tim]

hi hammonjj!

For which values of n≥2 does the implication:

axb=0 ⇔ a=0 or b=0
…
I know that this is true when n is a prime (answer in back of book), but I don't understand why. For example, if a=5 and b = 4, then that would also be 0 for n=5, right?

ah, but 5 = 0