Question

I will mark BRAINLIEST.............
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Show that the square of any odd integer is odd.

please explain.....

Answer 1

here is your answer ❤️............

13 is odd number and it's square is 169 it is also odd number

Answer 2

                 

As it is an odd number, the number leaves remainder 1 on division by 2.

So, let the number be  2n + 1,  for any integer n.

Squaring 2n + 1, we get,

⇒ (2n + 1)²

⇒ 4n² + 4n + 1

⇒ 4n(n + 1) + 1

⇒ 2(2n(n + 1)) + 1

Here, when we divide this  2(2n(n + 1)) + 1  by 2, we get  2n(n + 1)  as the quotient and 1 as the remainder.

As this leaves remainder 1, it is also an odd number.

Hence proved!!!

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