Question

Prove that the square of any positive integer is of the form 4q or 4q + 1 for some integer q.

Answer 1

SOLUTION :

Since positive integer n is of the form of 2m or 2m + 1

Case : 1

If n = 2m,then

n² = (2m)²

[On squaring both sides]

n²= 4m²

n² = 4q , where q = m²

Case :2

If n = 2m + 1,then

n² = (2m + 1)²

[On squaring both sides]

n² = (2m)² + 4m + 1²

[(a+b)² = a² + b² + 2ab]

n² = 4m² + 4m + 1

n² = 4m (m+ 1) + 1

n² = 4q + 1 , where q = m (m + 1)

Hence it is proved that the square of any positive integer is of the form 4q or 4q + 1, for some integer q.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Hope this helps you and please mark as brainliest.