(In reply to
Possible solution by broll)
Your elementary method is really cool, but since I dont see why x is invariably odd I just went and used the recurrence.
The fundamental (x1,y1) = (9,4) works
Forgive my lack of subscripts
xk+1 = x1xk + ny1yk
yk+1 = x1yk + y1xk
so for this we have
xk+1 = 9xk + 20yk
yk+1 = 9yk + 4xk
and the product xk+1*yk+1 simplifies to
36xk^2 + 161xkyk + 180yk^2
since 36, xkyk, and 180 are all divisible by 12 so does this sum.
So we have a recursive proof.

Posted by Jer
on 20101203 17:52:28 