# Groups in 2016

Algebra Level 4

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

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

Details and Assumptions:

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