# Integer-valued function

Is there any function (if any) f: Z -> Z such that
f(f(n))=-n , for every n belongs to Z(integers) ??

I think that there is not any function like the one described above but how can we prove it. Any ideas??

mathman

CRGreathouse
Homework Helper
Not integer-valued. (I assume if the OP meant Gaussian integers that would have been mentioned, since that's the obvious solution.)

I've been thinking about this for a few hours now and I can't see any way to do it, but I can't prove that it's impossible.

for n>0
f(2n-1)=2n
f(2n)=-2n+1
f(-2n+1)=-2n
f(-2n)=2n-1

f(0)=0

Nice, chronon. Nice.

matt grime