Proving an integer $3n+2$ is odd if and only if the integer $9n+5$ is even How can I prove that the integer $3n+2$ is odd if and only if the integer $9n+5$ is even, where n is an integer?
I suppose I could set $9n+5 = 2k$, to prove it's even, and then do it again as $9n+5=2k+1$
Would this work?

HINT $\rm\ \ 3\ (3\:n+2)\ -\ (9\:n+5)\:\ =\:\ 1$
Alternatively note that their sum $\rm\:12\:n + 7\:$ is odd, so they have opposite parity.
