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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.

See The Solution Submitted by Brian Smith    
Rating: 2.6667 (3 votes)

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Solution An algebraic solution | Comment 1 of 2
For every number n, n(n+2)+1 = (n+1), therefor for the series of odd numbers or the series of even numbers, any pair can be used as n and (n+2) therby fufilling the requirement of ab+1 for a=n and b=(n+2).
  Posted by Erik O. on 2004-06-23 08:26:26
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