Question

Show that the square of any odd integer is of the form 4q + 1 for some integer q

Answer 1

Answer:

Hey,

The answer of ur question is:

Step-by-step explanation:

Let q = m

Hence,

a = bm + r

let remainder will be 1...

a = 2m + 1

Squaring both side,

a ^2 = ( 2m + 1 )^2

a^2 = 4m^2 + 1 + 4m

a^2 = 4m^2 + 4m +1

a^2 = 4 ( m^2 + m ) +1

Let, (m^2 + m) = q....

Hence,

a^2 = 4q + 1...

Hope it helps u..

Have a nice day..☀✌✌..