- #1
MitsuZero
- 9
- 0
Homework Statement
[tex]\forall x\in Z,[/tex] if x is odd, [tex]\exists y\in Z,[/tex] such that [tex]xy\equiv1(mod 16)[/tex]
The attempt at a solution
I tried to prove this by using the fact that if you got a set of odd integers [tex]R = {1, 3, 5, ..., 15}[/tex], and if [tex]x, y, f(r) \in R[/tex], then [tex]xy\equiv f(r)(mod 16)[/tex]. This should directly imply that [tex]xy\equiv 1(mod 16)[/tex] (since 1 is an element of R).
I'm just about entirely lost at this point. I would really appreciate any help or guidance on how to proceed.
Thanks.
[tex]\forall x\in Z,[/tex] if x is odd, [tex]\exists y\in Z,[/tex] such that [tex]xy\equiv1(mod 16)[/tex]
The attempt at a solution
I tried to prove this by using the fact that if you got a set of odd integers [tex]R = {1, 3, 5, ..., 15}[/tex], and if [tex]x, y, f(r) \in R[/tex], then [tex]xy\equiv f(r)(mod 16)[/tex]. This should directly imply that [tex]xy\equiv 1(mod 16)[/tex] (since 1 is an element of R).
I'm just about entirely lost at this point. I would really appreciate any help or guidance on how to proceed.
Thanks.