The Parity Trick

Even and Odd. How hard could it be? 

Surprisingly, parity, when used well, can help us solve many challenging (and intriguing) proof problems in number theory down the road. For beginners, though, here are the basics that you should always bear in mind:

Even +(-) Even = Even

Odd   +(-) Odd   = Even 

Even +(-) Odd   = Odd

Even *  Even = Even

Odd   *  Odd   = Odd

Even *  Odd   = Even

2 is the only even prime!

1986 AJHSME: Problem 17

1989 AJHSME: Problem 25