Each of the numbers $a_{1},...,a_{n}$ is 1 or -1, and we have $$ S=a_1a_2a_3a_4+a_2a_3a_4a_5+...+a_na_1a_2a_3$$
Engel has written that if we replace any $a_i$ by $-a_i$ , then $S$ does not change $mod 4$; but I didn't get why.Could someone help me explain this?