This week's book giveaway is in the Mac OS forum. We're giving away four copies of a choice of "Take Control of Upgrading to Yosemite" or "Take Control of Automating Your Mac" and have Joe Kissell on-line! See this thread for details.

Each of a1,a2,a3..aN are either 1 or -1. The expression S = a1*a2*a3*a4+a2*a3*a4*a5+....+aN*a1*a2*a3 = 0 (* means multiplication and a1*a2 means value of a1 multiplied by value of a2) Prove that 4 divides N. I have taken this from Problem Solving Strategies

MH

Arjun Shastry
Ranch Hand

Joined: Mar 13, 2003
Posts: 1874

posted

0

If sign of every a(i) is changed,nothing changes .If sign of two a(i)s are same and other two are of different,nothing changes.If sign of one or three a(i) are different then S changes by +-4.If all four a(i) are of same sign,then S changes by +-8.That means S is changing by +-4 or +-8. S=0mod(4).But S = n hence 4 divides n.