Originally Posted by
Drexel28 You know that if $\displaystyle n\in\mathbb{N}$ that it may be represented as the product of primes $\displaystyle n=p_1^{\alpha_1}\cdots p_n^{\alpha_n}$, right? Well, except for $\displaystyle 2$ every prime is odd. So, we could for the sake of convenience write every integer as $\displaystyle n=2^{\beta}\cdot p_1^{\alpha_1}\cdots p_n^{\alpha_n}$ where $\displaystyle \beta$ may be zero of course. But, as previously mentioned since every other prime is odd and the product of odd numbers is odd it follows that $\displaystyle p_1^{\alpha_1}\cdots p_n^{\alpha_n}\text{ is odd}\implies p_1^{\alpha_1}\cdots p_n^{\alpha_n}=2m+1$ for some $\displaystyle m\in\mathbb{N}$, right? So now what?