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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 old fibo again Comment 2 of 2 |
take any 4 consecutive members of the following series: 1 3 8 21 55 etc ( every other number in fibonacci series 1 1 2 3 5 8 13 21 34 55 89...)
Clearly they qualify as a result of proven fib. features:    A(n)^2= A(n-1)*A(n+1)+1 for even n.

def;  A(0)=1;   A(1)=1;  A2=(2);  A(n)=A(n-1)+A(n-2)


Edited on August 16, 2010, 1:24 pm
  Posted by Ady TZIDON on 2004-06-23 08:30:59

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