How do we show that $(a_1+...+a_n)^2=(a_1^2+...+a_n^2)\mod 2$?
I can see that this works when there are two terms, but I have trouble visualizing the left hand expansion with infinite terms. I guess this could call for a proof by induction, but once I assume this is true for some $k$, I have no clue how to proceed for the $k+1$ case.
Just some tips or ideas would be appreciated.