Question

show that every positive integer is in the form of 2n and that every positive odd integer is of the form 2n + 1 when n is some integer

Answer 1

let a be any positive integer and b = 2
then by Euclid's algorithm, a=2n + r
for some integer q>or equal to 0
and r=0 or r =1
because 0<or equal to r <2
so a = 2n or 2n+1

if a is of the form of 2q, then a is an integer. also, a positive integer can be either even or odd. therefore, any positive odd integer is of the form 2q+1

Hope this will help you....