IMO Shortlist 1982 problem 7


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April 2, 2012
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Let p(x) be a cubic polynomial with integer coefficients with leading coefficient 1 and with one of its roots equal to the product of the other two. Show that 2p(-1) is a multiple of p(1)+p(-1)-2(1+p(0)).
Source: Međunarodna matematička olimpijada, shortlist 1982