help with modular arithmetic please

Hi all,

It is known that

from these we can say that if

or vice versa.

The same is true for the relationship between (c and d) and (e and f)

I have found that by using permutations of the above.

From reasonably extensive computer modelling of n, it also appears that but I can't seem to relate that to the above. Is it obvious why and I'm just suffering brain-freeze?

Thanks for helping thaw me out :)

Re: help with modular arithmetic please

Its pretty late, and I haven't really thought it all the way through but since 12 is the lcm of 3 and 4. Maybe you could convert the entire thing to mod 12.

Then build a relation table for a and b mod 12. Using a computer program you might be able to handle all the permutations, to find out what possible values n can hold mod 12. Of course you are expecting to see:

which then proves that:

Re: help with modular arithmetic please

Thanks takatok, I can do that. I was just hoping for something more elegant.