Question

showthattha square of any positive odd integer is of the form 4q+1whereq is any integer ​

Answer 1

We know that any positive odd integer of the form 2m +1 , 2m +3......
let a be any odd integer 
then 
a = 2m + 1

on squaring both sides we get 
a² = (2m +1)²
a² = 4m²+4m+1
a²= 4(m²+m) + 1. 
a² = 4q + 1. 
( where (m²+m) = q)

proved.....