Math, asked by SHUBHAM75757, 1 year ago

If x and y are two odd number then prove that x^2 + y^2 is not divisible by 4.

In equation form.

Answers

Answered by abhi178
1
x and y are odd numbers
let x = 2n +1
y = 2m + 1
where m , n are integers

now,
x² + y² = (2n +1)² +(2m +1)²

= 4n² + 4n + 1 + 4m² + 4m +1

= 4n² + 4m² + 4m + 4n +2

= 4{ m² + n² + m + n } + 2

if divide this by 4
we see that

4( m² + n² + m + n )/4 + 2/4

last term e.g 2/4 = 1/2 is fraction

hence, x² + y² isn't divisible by 4 when x and y are odd numbers.
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