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17 February, 15:18

F n and m are integers and n2 m2 is even, which of the following is impossible?

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  1. 17 February, 18:04
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    So, I think that you mean that

    n²+m² is even? (the "plus" sign is missing, but I think this is correct).

    this can only happen if either:

    both n and m are even

    or

    both n and m are odd

    That's because a sum of two expressions is even if either both or none of the expressions summed is even, and a power of a number is even only if the number is even too.

    are those some of the options?

    yes!

    n and m are even, - possible!

    n and m are odd, - possible!

    n+m is even, - possible; it would be the case i f either both n and m are even or both n and m are odd n+m is odd,

    so the option we'll choose is:

    none of these are impossible
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