Is it true that odd number raised to power (natural number) will always be odd? Is it true that odd number raised to power (natural number) will always be odd ? If this is true what is explanation behind this?
Thanks

Let $a^0=1$ be the base case. Then apply the inductive step $f(x)=ax$ (observe that $f^n(a)=a^n$). Clearly, this map preserves the parity, thus it must be odd.
