A Diophantine Equation | Find Integer Solutions.

[@SrisailamNavuluri]

By observation,x,y are positive odd numbers.
Otherwise 2022=2025-3=2025-4+1
=45^2-2^2+1=1+47×43=1+(43+4)43
=1+43×43+4×43=1^2+43^2+4×43.
(x,y)=(1,43) or (43,1) for positive integers.

[@mathsenhancersclass]

Thanks

[@LifeIsBeautiful-ki9ky]

x^2+4xy+y^2-2022=0
x=-2y(+/-)√(3y^2+2022)
Since x & y is an integer so discriminant is a perfect square
Take 3y^2+2022=z^2
z^2-3y^2=2022(Exercise for u )

[@mathsenhancersclass]

Thanks