In proof questions, what can any odd number be written as?

An odd number is a number indivisible by 2.

Therefore, an odd number could be written like this:

x is odd if x = 2n-1, n∈ℕ.

This basically means that x is equal to twice some number n (where n is a natural number), with 1 subtracted. This makes x an odd number because 2 times any natural number is an even number (so 2n is always an even number), and 1 subtracted from any even number is an odd number; therefore x = 2n-1 is odd.

If that is how you define x, you can then use it in your proof as any odd number.