Question

Show that any positive odd integer is of the form 2q+1 where q is some integer.

Answer 1

Answer:

let us assume a is positive odd integer

according to Euclid's division algorithm

a=bq+r where r is = to 0 or greater then 0 but smaller than b

here b=2

then possible value of r is 0,1

a=2q + 0.

but 2q+0 is divisible by 2 then it is even number but we assume a is positive odd integer

so a is not equal to 2q+0

a = 2q+1 it is not divisible by 2

so it is positive odd integer

hence prove