perplexus.info :: Sequences : Sequence of Squares

Sequence of Squares (Posted on 2004-06-23)

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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Puzzle Answer

Comment 3 of 3 |

Consider the numbers: 1,3,5 7 9,11,......

The product of any two consecutive terms is x^2-1.

Therefore, ab+1, bc+1, cd+1 ..... are all squares.

Posted by K Sengupta on 2023-08-22 06:32:51

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