Equation : x^2 ± k*y^2 are square numbers, k= 47, 53, 61, 79 and 101

 
      

Here are the first two sets of solutions:
 

 
 
Find solutions   for k = 47, 53, 61, and 79

Hint:

for   k = 47, 53, 61,   each requires a 15-digit number as the smallest value of x.
for   k = 79,   it requires a 17-digit number.