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.

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
Puzzle Answer	K Sengupta	2023-08-22 06:32:51
old fibo again	Ady TZIDON	2004-06-23 08:30:59
An algebraic solution	Erik O.	2004-06-23 08:26:26

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info