Question

Show that square of an odd positive integer is of the form 8m 1, for some integer m

Answer 1

Answer:

Hey friend

Step-by-step explanation:

Let us consider an odd positive no.

1

1²=8*0+1=1

3

3²=8*1+1=9

7

7²=8*6+1=49

11

11²=8*15+1=121 and so on.

So,here in each case you can see that

Every square of odd positive integer can be written in the form 8m+1 where m be any positive integer.

Hence proved

Hope it will help you

Answer 2

Answer:

let 'a' be any positive integer

a = 4q +1

squaring both sides

(a)²= (4q+1)²

a² = (4q)² + (1)² + 2(4q)(1)

a² = 16q² + 1 + 8q

a²=8(2q²+q) +1

here (2q²+q) = m

then

a²= 8m +1  

hence proved

Step-by-step explanation: