Sequence (A, B, C, D), (D – A) is a square number

 

Sequence a,b,c,d A3
 

D - A   ……….   ( \,A, \; B, \; C, \; D \,)

   2^2    …………    ( \,0, \; 1, \; 2, \; 2^2 \,)
   4^2    …………    ( \,0, \; 2^2, \; 8, \; 4^2 \,),   ( \,20, \; 5^2, \; 30, \; 6^2 \,)
   5^2    …………    ( \,56, \; 8^2, \; 72, \; 9^2 \,)
   6^2    …………    ( \,0, \; 3^2, \; 18, \; 6^2 \,)
   7^2    …………    ( \,240, \; 16^2, \; 272, \; 17^2 \,)
   8^2    …………    ( \,0, \; 4^2, \; 32, \; 8^2 \,),   ( \,80, \; 10^2, \; 120, \; 12^2 \,),   ( \,420, \; 21^2, \; 462, \; 22^2 \,)
   9^2    …………    ( \,40, \; 8^2, \; 88, \; 11^2 \,)

10^2   …………   ( \,0, \; 5^2 , \; 50, \; 10^2 \,),   ( \,21, \; 7^2, \; 77, \; 11^2 \,)
         …………   ( \,224, \; 16^2, \; 288, \; 18^2 \,),   ( \,1056, \; 33^2, \; 1122, \; 34^2 \,)
11^2   …………   ( \,1560, \; 40^2, \; 1640, \; 41^2 \,)
12^2   …………   ( \,0, \; 6^2, \; 72, \; 12^2 \,),   ( \,180, \; 15^2, \; 270, \; 18^2 \,)
13^2   …………   ( \,3080, \; 56^2, \; 3192, \; 57^2 \,)
14^2   …………   ( \,0, \; 7^2, \; 98, \; 14^2 \,),   ( \,165, \; 15^2, \; 285, \; 19^2 \,)
         …………   ( \,960, \; 32^2, \; 1088, \; 34^2 \,),   ( \,4160, \; 65^2, \; 4290, \; 66^2 \,)
15^2   …………   ( \,504, \; 24^2, \; 648, \; 27^2 \,)
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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