Groups in 2016

Algebra Level 2

Let (G,)(G,\circ) be a finite abelian group of order nn, say G={ai}i=1i=nG=\{a_i\}_{i=1}^{i=n}, where nn is a positive integer. Also, let x=a1a2an1anx=a_1\circ a_2\circ\cdots\circ a_{n-1}\circ a_n.

What is the value of x2016?x^{2016}?

Details and Assumptions:

  • eGe_G denotes the identity element of the group (G,)(G,\circ).
  • xn=xxxxn timesx^n=\underbrace{x\circ x\circ\cdots\circ x\circ x}_{n\textrm{ times}}.

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