Question

Show that the difference between any two consecutive square number in an odd number ​

Answer 1

Explanation:

4²=16

5²=25

25-16=9

9 is an odd number.

Answer 2

Any odd integer m is in the form

m=2k+1.

Let n and n+1 be consecutive integers. Then,

`(n+1)^2-n^2=n^2+2n+1-n^2=2n+1`