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28 March, 04:20

Prove that the difference of two odd integers is even. give a justification at each step.

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  1. 28 March, 06:26
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    Let a, b be two odd integers. Then both can be written as

    a=2k-1, k is an integer

    b=2m-1, m is an integer

    So,

    a-b=2k-1 - (2m-1) = 2k-2m-2=2 (k-m-1)

    Since, k and m and 1 are all integers, then (k-m-1) is also an integer. Hence, 2 (k-m-1) is an even integer.

    Thus, a-b is even.
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