{(a+b+c)^5 – a, (a+b+c+d)^5 – a}

 
 
(1)

Find three integers   a, \; b, \; c   such that

  (a+b+c)^5 \; - \; a
  (a+b+c)^5 \; - \; b
  (a+b+c)^5 \; - \; c

are all squares
 

(2)

Find four integers   a, \; b, \; c, \; d   such that

  (a+b+c+d)^5 \; - \; a
  (a+b+c+d)^5 \; - \; b
  (a+b+c+d)^5 \; - \; c
  (a+b+c+d)^5 \; - \; d

are all cubes.
 

(3)

Find three integers   a, \; b, \; c   such that

  (a+b+c)^4 \; - \; a
  (a+b+c)^4 \; - \; b
  (a+b+c)^4 \; - \; c

are all squares or all cubes.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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