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E=a^{2015}+b^{2015}+c^{2015}. if 2015 (a + b + c) =1, ab+bc+ca=2015abc

Source: 2015 Moldova JBMO TST p6

February 25, 2021
algebra

Problem Statement

Real numbers a,ba,b and cc satisfy the equalities 2015(a+b+c)=12015 (a + b + c) =1 and ab+bc+ca=2015abcab+bc+ca=2015 abc. Determine the numeric value of the expression E=a2015+b2015+c2015.E=a^{2015}+b^{2015}+c^{2015}.
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