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Prove that x and y are odd positive integers, then x2+ y2 is even but not divisible by 4.
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Prove that x and y are odd positive integers, then x2+ y2 is even but ...
Let the two odd numbers be 
(2a+1) & (2b+1) because if we add 1 to any even no. it will be odd.
x^2+y^2
=>(2a+1)^2+(2b+1)^2
=>(4a^2+4a+1)+(4b^2+4b+1)
=>4(a^2+b^2+a+b)+2
4 Is not a multiple of 2 it means clearly that 4 is not multiple of x^2+y^2, so x^2+y^2 is even but not divisible by 4.

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Prove that x and y are odd positive integers, then x2+ y2 is even but ...
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Prove that x and y are odd positive integers, then x2+ y2 is even but ...
Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1Hence x2 + y2 = (2k + 1)2 + (2p + 1)2 = 4k2 + 4k + 1 + 4p2 + 4p + 1 = 4k2 + 4p2 + 4k + 4p + 2 = 4(k2 + p2 + k + p) + 2Clearly notice that the sum of square is even the number is not divisible by 4.Hence if x and y are odd positive integers, then x2 + y2 is even but not divisible by 4.
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Prove that x and y are odd positive integers, then x2+ y2 is even but not divisible by 4.
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