Question

Show that the square of any positive odd integer is of the form 4q + 1. For some integer q.

Answer 1

Answer:

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.....