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.
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
old fibo again
