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Simplify terms

Source: 2013 Thailand October Camp Algebra and Functional Equations Exam p3

March 8, 2022
algebrasimplify

Problem Statement

Define ak=22k−2013+ka_k=2^{2^{k-2013}}+k for all integers kk. Simplify (a0+a1)(a1−a0)(a2−a1)⋯(a2013−a2012).(a_0+a_1)(a_1-a_0)(a_2-a_1)\cdots(a_{2013}-a_{2012}).
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