For some integer q, every odd integer is of the form

We know that an integer is said to be odd if it is not divisible by 2 .


Let m be a integer i.e. q = -1, 0, 1, 2, 3, 4,…..


Multiplying both the sides by 2


⇒ 2q = -2, 0, 2, 4, 6, 8,.……


Adding 1 on both the sides


⇒ 2q + 1 = -2 + 1, 0 + 1, 2 + 1, 4 + 1, 6 + 1, 8 + 1,…..


⇒ 2q + 1 = -1, 1, 3, 5, 7, 9,….


Hence, for some integer q, every even integer is of the form 2q + 1.

4