Thread: Odds and evens
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Old 2007-03-24, 00:55   #1
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Aug 2005

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Default 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.
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