Question

prove that if x and y are both odd positive integets then x2+y2 is even but not divisible by 4

Answer 1

Let x=2n+1(odd)
And y=2k+1
Therefore
x2+y2=(2n+1)^2 +(2k+1)^2
=4n^2 +4n+1+4k^2 +4k+1
=4(n^2 +n+k^2 +k) +2
=multiple of 4+2
It is even but not divisible by 4
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Answer 2

Answer:

Let the two odd positive no. be x = 2k + 1 and y = 2p + 1

Hence, x2 + y2 = (2k + 1)2 +(2p + 1)2

 = 4k2 + 4k + 1  + 4p2 + 4p +

  = 4k2 + 4p2 + 4k + 4p + 2

   = 4 (k2 + p2 + k + p) + 2

clearly, notice that the sum of square is even the no. is not divisible by 4

hence, if x and y are odd positive integer, then x2 + y2 is even but not divisible by four.

Step-by-step explanation:

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