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

 
Fibonacci numbers are the numbers in the following integer sequence :

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, …

 
SEQUENCE a,b,c,d 1
 

   13   ……….   ( \, 12, \; 4^2, \; 20, \; 5^2 \, )

   34   ……….   ( \, 15, \; 5^2, \; 35, \; 7^2 \, )
   34   ……….   ( \, 110, \; 11^2, \; 132, \; 12^2 \, )

   55   ……….   ( \, 306, \; 18^2, \; 342, \; 19^2 \, )

  144   ……….   ( \, 180, \; 15^2, \; 270, \; 18^2 \, )

  610   ……….   ( \,119, \; 17^2 , \; 459, \; 27^2 \,)
  610   ……….   ( \, 9999, \; 101^2 , \; 10403, \; 103^2 \,)
  610   ……….   ( \,41006, \; 203^2 , \; 41412, \; 204^2 \,)

1597   ……….   ( \,282492, \; 532^2 , \; 283556, \; 533^2 \,)

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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