The problem: Let x be an element of the integers. If 2^(2x) is an odd integer, then 4^x is an odd integer.
This problem was different from the previous direct proof problems we were assigned and I'm not sure if the phraseology is correct or not. Here is my proof:
"Let x be an element of the integers. Assume 2^(2x) is an odd integer. Obviously 2^(2x) = 4^x. For x < 0, 4^x is neither even nor odd. For x greater than or equal to 0, 4^x is even except when x=0. Since 0 is an element of the integers it follows that 4^x is odd."