For how many unique coordinate points (p, q), such that p and q are integers, is it true that p2 - q2 = 1155?

Hello,

1155=3*5*7*11

3,5*7*11
5,3*7*11
7,3*5*11
11,3*5*7

3*5,7*11
3*7,5*11
3*11,5*7

7 cases:

1) p+q=5*7*11
   p-q=3
   ==>p=(5*7*11+3)/2=194
   ==>q=(5*7*11-3)/2=191
   194²-191²=1155   Solution 1.
  
2) p+q=3*7*11
   p-q=5
==>p=  118
==>q= 113
    118²-113²=1155 Solution 2.
   
3) p+q=3*5*11
   p-q=7
==>p= 86
==>q= 79
    86²-79²=1155  Solution 3.
   
4) p+q=3*5*7
   p-q=11
==>p=  58
==>q=  47
    58²-47²=1155 Solution 4.
   
5) p+q=7*11
   p-q=3*5
==>p= 46
==>q= 31
    46²-31²=1155 Solution 5.
   
6) p+q=5*11
   p-q=3*7
==>p= 38
==>q= 17
    38²-17²=1155 Solution 6.
   
7) p+q=5*7
   p-q=3*11
==>p= 34
==>q=  1
    34²-1²=1155
   

   
   

   

  

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