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Prove that if X and y are odd positive integers, then x2 +y2 is even but not divisible by 4?

    • Posted by Gaurav Kaushik 7 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Susai Raj 7 years, 6 months ago

    x and y are odd integers. So they should be of the form x= 2m+1, y= 2n+1 for some integers m and n.
    x^2 + y^2 =(2m+1)^2 + (2n+1)^2
    =4m^2+4m +1+4n^2+4n+1
    =4m^2+4n^2+4m+4n+2
    =4(m^2+n^2+m+n) + 2
    Which is an even number but not divisible by 4.

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