There simply is NONE. You sure your question is CORRECTLY worded?
Positive integers are both relatively prime and less than or equal to 2008. is a perfect square.
has the same digits as in the reverse order. The number of such ordered pairs is _________ .
I started with 2 digits:
Let and
which can't be factorized and isn't a perfect square.
Tried the same with 3 digits and ended up with this:
This also isn't factorizable.
I've simply got no idea of how to proceed from here.
I am not sure but my answer is zero !
It is a famous property ( which is not what i am confused ) , , the proof is as follows :
Let
so and
We have
Since coprime , they can be expressed as , wlog let so we have
I consider the form whether it can be the multiple of
Be caution the quadratic residues are so , since the intersection of the sets is just , we conclude iff . Therefore , which is false because , so we can never find out any odered pair .
EDIT: I have made it more complicated , in fact we can consider the quadratic residues from here :
It is easy to show since we have already proved that , so we have :
consider the residues as i mentioned .