Prove the following Let a and b be any integers If n is an o

Prove the following: Let a and b be any integers. If n is an odd integer the n2 is an odd integer.

Solution

The general from of an odd nuber is 2n+1

Where n is an integer.

Let 2a+1 and 2b+1 are two odd integers

Where a and b belongs to z

TTheir product =(2a+1)(2b+1)

=2a (2b+1)+2b+1

   =4ab+2a+2b+1

   =2(2ab+a+b)+1

n2=2×integer+1

n2 =an odd integer