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AMO 2027 Grades 9-11 SET 2 - Self-study Question 14

AMO · AMO 2027 Grades 9-11 SET 2 - Self-study

Question 14

Given $$x^4+x^3+x^2+x+1=0,$$ find the value of $x^{2021}$.
Treat $x$ as an algebraic or complex number satisfying the equation; a real solution is not assumed. Preserve the printed target exactly. For this edition, enter the simplest expression in terms of $x$, using a lowercase letter, rather than forcing a numerical value.