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23 April, 12:16

Difference between the squares of two consecutive numbers is not divisible by 2

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  1. 23 April, 14:40
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    Hmm, let's prove that

    consecutive integers are even then odd or odd then even

    all even integers can be represented by 2n where n is an integer

    all odd integers can be represetned by 2n+1 or 2n-1

    all numbers divisible by 2 are even

    alright

    we wil start with even then odd

    2n and 2n+1 are our even and odd numbes, the

    their square are 4n² and 4n²+4n+1 respectively

    their difference is 4n+1 or 2n+2n+1, an even+an odd, resulting in an odd difference

    lets try odd then even

    odd is 2n-1 and the even is 2n

    their square are 4n²-4n+1 and 4n² respectively

    their difference is 4n-1 which is 2n+2n-1, another even+odd combo, resulting in an odd difference

    proven, the difference between the squares of 2 consecutive numbers is not divisible by 2
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