X and y are integers Then what are the possible values of x^2 - y^2 - Maths - Mathematical Reasoning

Question

X and y are integers Then what are the possible values of x^2 - y^2
(I mean what would be the conditions) For example, for x^2 - y^2 =
12345678, there is no integral values of X and y ( pls explain this
question as well along)

Vivek Rai · Accepted Answer

Dear student
There is no such condition,for which we can judge the possible
values of x2-y2 For this particular Question,
we have, x2-y2=12345678, R H
S is an even number so both the x and y must be even or odd, In either of the case the Number must be divisible by 4 as if the numbers are odd, we can write them as 2m+1and 2n+1so x2-y2=(x+y)(x-y)={2(m+n+1)}{2(m-n)}=4times some integer if the numbers are even, we can write them as 2mand 2n
so x2-y2=(x+y)(x-y)={2(m+n)}{2(m-n)}=4times some integer but R
H
S is not divisible by 4 so we can say this particular equation does not have any solution
Hope this clears your doubt
With regards

X and y are integers. Then what are the possible values of x^2 - y^2.... (I mean what would be the conditions)....... For example, for x^2 - y^2 = 12345678, there is no integral values of X and y.. ( pls explain this question as well along)