Hi all,

$\displaystyle n=((a^2+b^2)(c^2+d^2)(f^2+2ef-e^2))^2+((a^2+b^2)(d^2+2cd-d^2)(e^2+f^2))^2+(b^2+2ab-a^2)(c^2+d^2)(e^2+f^2))^2$

It is known that

$\displaystyle a^2+b^2\equiv 1\ mod\ 4$

$\displaystyle c^2+d^2\equiv 1\ mod\ 4$

$\displaystyle e^2+f^2\equiv 1\ mod\ 4$

from these we can say that if

$\displaystyle a\equiv(0\ mod\ 4)\ or\ (2\ mod\ 4)\ then\ b\equiv\ (1\ mod\ 4)\ or\ (3\ mod\ 4)$ or vice versa.

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

I have found that $\displaystyle n\equiv\ 3\ mod\ 4$ by using permutations of the above.

From reasonably extensive computer modelling of n, it also appears that $\displaystyle n\equiv0\ mod\ 3$ 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