How to find a solution to this equation so the result is a perfect square ?

[Laël Cellier <lael.cellier@laposte.net>]

Bonjour,
simple question, I’ve the following expression : (y² + 
X×53919893334301279589334030174040979997534463873026188556492192357233)÷20422354090808007360481140437163150058277495681745577657420405131241
for example, 
X=102111770454040036802405702185845298473875351094786902380116798296 and 
y=21 leads to 
269599466671506397946670150870282914247971805150249613489807500649 which 
is the perfect square of 519229685853482762853049632922093

I want to find 1 or more set of integer x and y such as the end result 
is a perfect square. But how to do it if the divisor is different than 
20422354090808007360481140437163150058277495681745577657420405131241 ?
Cordialement,