Question

show that every positive even integer is in the form of 2 power n

Answer 1

Let a be any positive integer and b = 2

By Euclid's theorem a = 2q + r where 0 is less than or equal to r and that is = b(2)

All possible values of r are 0 and 1

a=2q + 0 =2q

a=2q + 1

If a is in form 2q then it is even

A positive integer can be either odd or even

So we conclude that a positive odd integer is 2q+1