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Composite sum

Source: INDIA IMOTC-2006 TST1 PROBLEM-2; IMO Shortlist 2005 problem N3

June 3, 2006
algebrapolynomialnumber theorycomposite numberprime numbersIMO ShortlistHi

Problem Statement

Let a a, b b, c c, d d, e e, f f be positive integers and let S=a+b+c+d+e+f S = a+b+c+d+e+f. Suppose that the number S S divides abc+def abc+def and ab+bc+ca−de−ef−df ab+bc+ca-de-ef-df. Prove that S S is composite.
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