Prove that the Square of any Odd Integer is Odd

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Prove that the Square of any Odd Integer is Odd

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Okay, my stats Professor told us to remember that you represent odd numbers with the expression 2N+1. That is because if N is an even number, then being multiplied by 2 doesn't change that, but adding 1 to it makes it odd. So I will use the expression 2N+1 to be my universally generalized ODD NUMBER. When we square that we get 4N^2+4N+1. Let's take that apart: in the first element whether N^2 is odd or even multiplying it by a factor of 2 makes it even. The same for the second expression, where whether N is odd or even multiplying it by a factor of 2 makes it even. Look at the last element of the SUM: BINGO! It's a 1 and if you add one to any sum of even numbers you will get an odd number. Since it is TRUE of a universal generality of for any Odd Number it is TRUE for every Odd Number.

leovolont

Odd n means that n ≡ 1 (mod 2) that is n^2 ≡ 1 (mod 2), QED.

raffaelevalente

Why do you say odd "integer?" Isn't an odd number an integer by definition? I'm just a Calculus 2 student, so please forgive my ignorance.

iamthebullSH

Try to speak in hindi it will more easy to understand because your English is

Kashishmalikk

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