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Sequence of Squares (Posted on 2004-06-23) Difficulty: 2 of 5
Show that there is an infinite sequence of distinct positive integers a, b, c, d, ... for which ab+1, bc+1, cd+1, ... are all squares.

  Submitted by Brian Smith    
Rating: 2.6667 (3 votes)
Solution: (Hide)
The sequence can be 1,3,5,7,9,... or 2,4,6,8,10,...

In both sequences the product of two consecutive terms is of the form x^2-1, so by adding 1, the result is a square.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutionold fibo againAdy TZIDON2004-06-23 08:30:59
SolutionAn algebraic solutionErik O.2004-06-23 08:26:26
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