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TOT 1999 Autumn OJ2 d = a^{1999} + b^{1999} + c^{1999} when a + b + c = 0

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May 11, 2020
number theoryprimeSum of powersSum

Problem Statement

Let d=a1999+b1999+c1999d = a^{1999} + b^{1999} + c^{1999} , where a,ba, b and cc are integers such that a+b+c=0a + b + c = 0. (a) May it happen that d=2d = 2? (b) May it happen that dd is prime?
(V Senderov)
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