Question

prove that if x and y are both positive integers then x square plus y square is even but not divisible by 4

Answer 1

Step-by-step explanation:

Since x and y are odd positive integers, so let x = 2q + 1 and y = 2p + 1 ,

•°• x² + y² = ( 2q + 1 )² + ( 2p + 1 )² .

= 4( q² + p² ) + 4( q + p ) + 2 .

= 4{( q² + p² + q + p )} + 2 .

= 4m + 2 , where m = q² + p² + q + p is an integer .

•°• x² + y² is even and leaves remainder 2, when divided by 4 that is not divisible by 4.

Hence, it is solved

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Answer 2

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