- #1
Bashyboy
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- 5
Homework Statement
Prove that if ##\sigma## is the ##m##-cycle ##(a_1 ~ a_2 ... a_m)##, then for all ##i \in \{1,...,m\}##, ##\sigma^{i}(a_k) = a_{k+i}##, where ##k+i## is replaced by its least positive residue ##\mod m##.
Homework Equations
The Attempt at a Solution
My question is embarrassingly simple. What is the least positive residue? Would it be that number ##x \in \mathbb{Z}^+## for which ##x \equiv k+1 (\mod m)##?