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9 September, 22:48

If nn and mm are integers and n2+m2n2+m2 is even, which of the following is impossible?

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  1. 9 September, 23:10
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    Given:

    n and m are integers

    n² + m² is even.

    Choices:

    a) n and m are even

    b) n and m are odd

    c) n + m is even

    d) n + m is odd

    e) none of these are impossible.

    let us assume:

    n and m are even. 2² + 4² = 4 + 16 = 20 even.

    n and m are odd. 3² + 5² = 9 + 25 = 34 even

    n + m is even : 2 + 4 = 6; 3 + 5 = 8 even

    Using the assumption as basis, D.) n + m is odd is impossible.
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