Question

x²+y² is an eve integer but not divisible by 4

Answer 1

Solution:

x²+y² is even in integer but not divisible by 4

It can be possible when x=1 and y= 1

or x = 0 and y= 0
or x= -1 and y= -1

Hence the number can be

1²+1² = 2

OR

0²+0² = 0

OR

(-1)²+(-1)² = 2

Hence number can be 0 or 2

Answer 2

Heya User,

--> Ummm, let's say -> 

--> Suppose 'x' is odd.. => x² is odd

However, if [ x² + y² ] is even, => y² is odd => y = odd
Similarly, if -> x² is even => y² is even too

--> A happy observation -->
  ---> If x² is even => x is even 
==> '2' divides 'x' => 'x' is of the form --> 2k 
==> x = 2k  => x² = 4k²

However, if 'x' is even, y is even from ^_^ { above hypothesis }
=> y = 4m²

=> [ x² + y² ] = 4 [ k² + m² ]  ---> implies that :->

" Both of the integers cannot be even "
=> " x and y are odd "

Now,
 --> let x = 2a + 1 ; y = 2b + 1
=> [ x² + y² ] = [ 4a² + 4b² + 4a + 4b + 2 ]
=> [ x² + y² ] = 2 [ 2a² + 2b² + 2a + 2b + 1 ]

=> 2 divides [ x² + y² ] but 4 does not..

And hence, we conclude that --> 'x' and 'y' are odd integers