DAILY MATHS CHALLENGE #2

i guess the obvious thing that follows from 0=1+...+1 is that any element, combined n times with itself using + is zero, so you have

-x+....+-x = (-1)x + .... + (-1)x

but i can't figure how to make the extra terms go away.

this is tough. any way that you use 0 = 1+....+1 you end up with a mess of extra terms that are hard to deal with.

how long is the proof?