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

1.	Show that the square of any odd integer is in the form 4q+1 for some integer q.
Answer» 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 Step-by-step EXPLANATION: on SQUARING both SIDES we get a² = (2m +1)² a² = 4m²+4m+1 a²= 4(m²+m) + 1. a² = 4q + 1. and (m²+m) = q

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

Answer»

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

Step-by-step EXPLANATION:

on SQUARING both SIDES we get

a² = (2m +1)²

a² = 4m²+4m+1

a²= 4(m²+m) + 1.

a² = 4q + 1.

and (m²+m) = q

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

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