# Square element

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Suppose $(S,*)$ is a magma, i.e., $S$ is a set and $*$ is a binary operation on $S$. Then, an element $x \in S$ is termed a square element or square if there exists $y \in S$ such that $x = y * y$.
Note that $S$ may be a group or semigroup, which is the typical context of use; however, the notion of square element makes sense even for non-associative binary operations.