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Prove that if x and y are odd positive i...

Prove that if `x and y` are odd positive integers, then `x^2+y^2` is even but not divisible by 4.

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Knowledge Check

  • If x and y are positive integers and (2x +y) is even, which of the following must be even ?

    A
    `x^(3) + 2xy^(2)`
    B
    `3x^(2) + 2y`
    C
    `4x^(2) + x + y^(2)`
    D
    `5x^(2) + x + y^(3)`

  • If x and y are positive integers and sqrt(x) = y + 3 ,then what is the value of y^(2) ?

    A
    `x-9`
    B
    `x+9`
    C
    `x-6sqrt(x)+9`
    D
    `x^(2)-6sqrt(x)+9`

    • Similar Questions

    Explore conceptually related problems

    If n is an odd positive integer, show that (n^2-1) is divisible by 8.

    Prove that n^2-n divisible by 2 for every positive integer n.

    (x)/(8)+(y)/(5)=(31)/(40) In the equation above, if x and y are positive integers, what is the value of x+y?

    If x, y, and z are consecutive integers, is x+y+z divisible by 3?

    Check the validity of the following statement. If x and y are odd integers, then xy is an odd integer.

    Prove that the product of two consecutive positive integers is divisible by 2.

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