- #1
Cryphonus
- 60
- 0
Hey;
im kind of stuck with the following question, i would be glad if you can help
Determine if the function f : Z x Z --> Z defined by f(m, n) = m^2 + n^2 is one-to-one.
if F(x1) = F(x2) implies x1=x2 then the function is one to one.
i did some algebra and ended up with the equation;
(m1-m2)(m1+m2) = (n2-n1)(n2+n1)
i don't know how to disprove the equality from this point
im kind of stuck with the following question, i would be glad if you can help
Homework Statement
Determine if the function f : Z x Z --> Z defined by f(m, n) = m^2 + n^2 is one-to-one.
Homework Equations
if F(x1) = F(x2) implies x1=x2 then the function is one to one.
The Attempt at a Solution
i did some algebra and ended up with the equation;
(m1-m2)(m1+m2) = (n2-n1)(n2+n1)
i don't know how to disprove the equality from this point