Thread: Odds and evens View Single Post
 2007-03-24, 00:55 #1 fetofs     Aug 2005 Brazil 36210 Posts Odds and evens You have three sequences A = a1, a2,...,an, B = b1, b2,...,bn and C = c1, c2,...,cn. For each 1 <= i <= n it is known that at least one of ai, bi and ci is odd. Prove that there are integers r, s and t such that rai + sbi + tci is odd for at least $\frac{4n}7$ values of i.